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\usepackage{amsmath,amssymb,amsfonts} % AMS LateX is standard nowadays.
\usepackage{ifthen} % For \ifthenelse{cond}{true}{false}.
\usepackage{graphics} % For picture environment.
\usepackage{graphicx} % For picture environment.
\usepackage{rotating} % For words at an angle.
\usepackage{colortbl} % Colouring table rows and columns. Digital Typography. p. 295.
\usepackage{fancyhdr} % For underlined headings.
\usepackage{sprite} % Useful for creating small objects.
\usepackage{picinpar} % For pictures in paragraphs. Use with care.
% Symbols, fonts, etc.
\usepackage{textcomp} % Includes the euro symbol \texteuro.
\usepackage{wasysym} % Symbols: Digital Typography, section 3.2.2.
\usepackage{latexsym} % Symbols.
%\usepackage{cyrillic} % Cyrillic. See C:\ADF\cyrillic.pdf. Requires file `cyrillic.sty.
\usepackage{arabtex} % Arabic, Hebrew, etc. See C:\ADF\ArabTex.PDF. See M500 249 for simple example.
% More packages
\usepackage{fp} % For floating point calculations
\usepackage{booktabs} % Suggested by Reinhardt Messerschmidt
\usepackage{enumerate} % Suggested by Reinhardt Messerschmidt
\usepackage{tikz} % Suggested by Reinhardt Messerschmidt
\usetikzlibrary{calc,decorations.markings,intersections,arrows}
\usepackage{algpseudocode} % For displaying algorithms (suggested by Roger Thompson)
\usepackage{mathdots} % Various forms of dots
\usepackage[colorlinks=false,urlbordercolor={0 0 1},linkbordercolor={1 1 1},citebordercolor={1 1 1}]{hyperref}
% Gives the URL specified in \url{} a blue border and makes it clickable in the PDF file
% I can't get it to work for page references.
\usepackage{setspace} % Control line spacing with, say \begin{spacing}{0.9} blah blah \end{spacing}.
\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}{Proposition}
% Real top-left is at (-25.4mm, -25.4mm).
% We will do everything relative to (-25.4mm, -25.4mm), i.e. the corner of the paper.
% Total width 297.0mm, centre line 148.5mm.
%\hoffset -25.4mm \voffset -25.4mm
\hoffset -26.0mm \voffset -22.0mm % Mystery: Why did I change this?
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\evensidemargin 16.75mm
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% Fonts for very small stuff
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\newfont{\mfhfnanoit}{cmssi1 scaled\magstep0}
% Font for big first letter
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% Font for 9-point text
\newfont{\mfhfnine}{cmr9 scaled\magstep1}
%
% Six Cyrillic fonts:
%
% cyrrm = "Roman", or really upright, normal font
% cyrit = Italic (cursive forms of letters)
% cyrsl = Italic (non-cursive forms of letters)
% cyrsf = Sans-serif
% cyrbf = Bold-face
% cyrsc = Small capitals
%
\newcommand{\cyrrm}{\fontencoding{OT2}\selectfont\textcyrup}
\newcommand{\cyrit}{\fontencoding{OT2}\selectfont\textcyrit}
\newcommand{\cyrsl}{\fontencoding{OT2}\selectfont\textcyrsl}
\newcommand{\cyrsf}{\fontencoding{OT2}\selectfont\textcyrsf}
\newcommand{\cyrbf}{\fontencoding{OT2}\selectfont\textcyrbf}
\newcommand{\cyrsc}{\fontencoding{OT2}\selectfont\textcyrsc}
% M500 macros. All start with \mfh
% Reset to the standard gap between paragraphs.
% Syntax: \mfhparskip
\newcommand{\mfhparskip}{\parskip 1mm}
% Title of an article.
% Syntax: \mfhtitle{title}
\newcommand{\mfhtitle}[1]{{\noindent \mfhftitle #1} \mfhparskip \normalsize}
% Title of an article in italics.
% Syntax: \mfhsmtitleit{title}
\newcommand{\mfhtitleit}[1]{{\noindent \mfhftitleit #1} \mfhparskip \normalsize}
% Title of an article in a smaller font.
% Syntax: \mfhsmtitle{title}
\newcommand{\mfhsmtitle}[1]{{\noindent \mfhfsmtitle #1} \mfhparskip \normalsize}
% Title of an article in italics and in a smaller font.
% Syntax: \mfhsmtitleit{title}
\newcommand{\mfhsmtitleit}[1]{{\noindent \mfhfsmtitleit #1} \mfhparskip \normalsize}
% Author.
% Syntax: \mfhauthor{author-name}
\newcommand{\mfhauthor}[1]{%
\vskip 1mm%
\noindent {\mfhfauthor #1}%
\mfhparskip \normalsize}
% Title of a letter.
% Syntax: \mfhletter{letter title}
\newcommand{\mfhletter}[1]{{\vskip0.2cm\noindent\mfhfletter #1}\mfhparskip}
% A long line to end an article.
% Syntax: \mfhendarticle
\newcommand{\mfhendarticle}{\vskip 2mm\hrule}
% A medium line to end an author.
% Syntax: \mfhendauthor
\newcommand{\mfhendauthor}{\noindent\hspace*{2cm}\hrulefill\hspace*{2cm}}
% A short line to end a part of an article.
% Syntax: \mfhendpart
\newcommand{\mfhendpart}{\vskip -2mm\noindent\hspace*{4cm}\hrulefill\hspace*{4cm}}
% Generate a list with a fixed specified item width. See Burger, p. 28.
% Syntax: \begin{mfhlist}{width-defining-text}
% \item[label] text for item
% ...
% \item[label] text for item
% \end{mfhlist}
\newcommand{\mfhlistlabel}[1]{\mbox{#1}\hfil}
\newenvironment{mfhlist}[1]{%
\begin{list}{}
{
\let\makelabel\mfhlistlabel
\settowidth{\labelwidth}{#1}
\setlength{\leftmargin}{\labelwidth}
} }{%
\end{list}}
% Indented text (e.g. for stating a problem prior to giving the solution).
% Syntax: \mfhindent{text}
\newcommand{\mfhindent}[1]{%
\begin{list}{}{%
\setlength{\rightmargin}{\leftmargin}
\setlength{\itemsep}{0cm}
\setlength{\parsep}{0cm}
\setlength{\topsep}{0cm}}
\item{#1}
\end{list}}
% A General macro for indented text, which allows the lh-margin and text width to be specified.
% Syntax: \mfhgenindent{lh-margin-width}{text-width}{text}
\newcommand{\mfhgenindent}[3]{\noindent\hspace*{#1}\begin{minipage}{#2}{#3}\end{minipage}}%
% Special form of indentation for quotations, etc.
% Syntax: \mfhquotation{text}
\newcommand{\mfhquotation}[2]{%
\begin{list}{}{%
\setlength{\rightmargin}{\leftmargin}
\setlength{\itemsep}{0cm}
\setlength{\parsep}{0cm}
\setlength{\topsep}{0cm}}
\item{\em#1}
\ifthenelse{\equal{#2}{}}{}{\item{\hfill #2}}
\end{list}}
% Centre a single line of text without creating gaps at top and bottom.
% Syntax: \mfhcentre{text}
\newcommand{\mfhcentre}[1]{\noindent\parbox{\textwidth}{\centering #1}}
% Create a centred block of text of a given width.
% Suitable for poetry.
% Syntax: \mfhverse{width}{lines of poetry}
\newcommand{\mfhverse}[2]{
\begin{center}
\begin{minipage}{#1}
{#2}
\end{minipage}
\end{center}
}
% Define a counter.
\newlength{\mfhW}
% Make an empty box of the same width as a piece of text.
% Syntax: \mfhemptybox{text}
\newcommand{\mfhemptybox}[1]{\settowidth{\mfhW}{{#1}}\makebox[\mfhW]{}}
% Absolute value notation |x|.
% Syntax: \mfhabs{x}
\newcommand{\mfhabs}[1]{\left|#1\right|}
% (mod x).
% \mfhmod{x} (mod x).
% \pmod{x} (mod x) %(redefinition).
% \mod mod %(redefinition).
% Why not use the original \mod and \pmod commands? BECAUSE THEY DON'T WORK!
\newcommand{\mfhmod}[1]{~(\mathrm{mod}~#1)}
\renewcommand{\pmod}[1]{~(\mathrm{mod}~#1)}
\renewcommand{\mod}{\mathrm{~mod~}}
% Trigonometric and hyperbolic functions that do not seem to be built in.
% Syntax: \function
\newcommand{\cosec}{\mathop{\mathrm{cosec}}}
\newcommand{\arccosh}{\mathop{\mathrm{arccosh}}}
\newcommand{\arcsinh}{\mathop{\mathrm{arcsinh}}}
\newcommand{\arctanh}{\mathop{\mathrm{arctanh}}}
% Symbols to indicate the real and imaginary parts of a complex number; e.g. Re and Im.
% A sensible alternative to those terrible Gothic symbols.
% Syntax: \mfhRe
\newcommand{\mfhRe}{\mathop{\mathrm{Re}}}
% Syntax: \mfhIm
\newcommand{\mfhIm}{\mathop{\mathrm{Im}}}
% A strut for use in a table in the line below a horizontal line.
% Syntax: \mfhs
\newcommand{\mfhs}{\rule{0mm}{4mm}}
% A square box to mark the end of a proof.
% Syntax: \mfhQED
\newcommand{\mfhQED}{~ \hspace*{\fill}$\square$}
% Space between factors.
% This command used by Mathematica TeXForm.
% Syntax: \multsp
\newcommand{\multsp}{\,}
% x above y.
% Syntax: \mfhover{x}{y}
\newcommand{\mfhover}[2]{\genfrac{}{}{0mm}{0}{#1}{#2}}
% matrix [...].
% Syntax \mfhbmatrix{A11 & A12 & ... \\ A21 & A22 & ... \\ ...}
\newcommand{\mfhbmatrix}[1]{\left[\begin{matrix}#1\end{matrix}\right]}
% matrix (...).
% Syntax \mfhpmatrix{A11 & A12 & ... \\ A21 & A22 & ... \\ ...}
\newcommand{\mfhpmatrix}[1]{\left(\begin{matrix}#1\end{matrix}\right)}
% x/y.
% Used when I can't make up my mind how to do a fraction: \dfrac{x}{y} or one of x/y, (x)/y, x/(y), (x)/(y).
% Syntax: \mfhdfrac{numerator}{denominator}
% Syntax: \mfhsfrac{numerator}{denominator}
% Syntax: \mfhpsfrac{numerator}{denominator}
% Syntax: \mfhspfrac{numerator}{denominator}
% Syntax: \mfhpspfrac{numerator}{denominator}
\newcommand{\mfhdfrac}[2]{\dfrac{#1}{#2}}
\newcommand{\mfhsfrac}[2]{#1/#2}
\newcommand{\mfhpsfrac}[2]{(#1)/#2}
\newcommand{\mfhspfrac}[2]{#1/(#2)}
\newcommand{\mfhpspfrac}[2]{(#1)/(#2)}
% Those dreaded fractions for constructions like 1/4 with the numerator up and the denominator down, and slightly smaller.
% Use the second alternative if there is an integer, as in, for example, 365 1/4.
% Syntax: \mfhfrac{numerator}{denominator}
% Syntax: \mfhintfrac{integer}{numerator}{denominator}
\newcommand{\mfhfrac}[2]{\raisebox{0.8mm}{\small #1}\hspace{-0.4mm}\raisebox{0.4mm}{/}\hspace{-0.3mm}\raisebox{-0.3mm}{\small #2}}
\newcommand{\mfhintfrac}[3]{#1\hspace{0.25mm}\mfhfrac{#2}{#3}}
% A tilde for those cases where Web addresses insist on using it.
% This appears in a PDF file as a standard ASCII tilde.
% Syntax: \mfhtilde
\newcommand{\mfhtilde}{{\large\raisebox{-1.7mm}{\textasciitilde{}}}}
% Omit x in its entirety. Use whilst being indecisive about using the enclosed material.
% Syntax: \mfhnull{x}
\newcommand{\mfhnull}[1]{}
% Change the baseline skip value.
% This is used to squeeze an article into a space that would normally be insufficient.
% Check the scope of the \mfhbls command before changing 10.0mm to something suitable.
% Syntax:
% \renewcommand{\mfhbls}{\baselineskip 10.0mm}{\mfhbls
% xxx lines of text xxx
%
% } % Leave a blank line before the closing brace. Why? Because otherwise it screws up.
%
% {\mfhbls
% xxx more text xxx
%
% } % Leave a blank line before the closing brace.
%
% ...
\newcommand{\mfhbls}{\baselineskip 10.0mm}
% Change the line spacing.
% This is used to squeeze an article into a space that would normally be insufficient.
% A possibly more suitable alternative to above
% Syntax:
% \begin{spacing}{expansion factor}
% blah blah
% \end{spacing}
%
% Redefine \section commands to save the awful wastage of space by the usual LaTeX \section command.
% There might be a `proper' way to do this. However, for now I will rename \section to \mfhsection.
%
% For this to work properly, change
% \section{blah blah}
% to
% \mfhsection{blah blah}%
%
% Note that the % at the end prevents an unwanted space appearing on the next line.
%
\newcounter{mfhsection}
\setcounter{mfhsection}{0}
\newcommand{\mfhsection}[1]{\stepcounter{mfhsection}\vskip 1mm
\noindent {\bf \themfhsection~~#1}%
\vskip 0mm
\noindent}
\parindent 6mm
\pagestyle{empty}
\parindent 0mm
\begin{document}
\pagestyle{fancy}
\lhead[\sf Page \thepage]{}
\chead[{\sf M500 \rm 000}]{{\sf M500 \rm 000}} %!!!
\rhead[]{\sf Page \thepage}
\lfoot[]{}
\cfoot[]{}
\rfoot[]{}
\parindent 6mm
\raggedbottom % Ensures uniform paragraph spacing.
\sloppy % Loose lines preferred to trespassing into the right margin.
\setcounter{page}{1}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vskip 5mm
{ %******% START OF ITEM %******%
\setcounter{equation}{0}
\setcounter{theorem}{0}
\setcounter{lemma}{0}
\setcounter{table}{0}
\setcounter{figure}{0}
\setcounter{mfhsection}{0}
\newcommand{\mfhcarrot}{\raisebox{-1.5mm}{\Large \textasciicircum}}
\newcommand{\mfhAdvGap}{\vskip 2.5mm}
\newpage
\mfhtitle{Advice for authors}
\mfhauthor{Tony Forbes}
\noindent We welcome mathematical contributions to {\sf M500} at any level from trivia to serious research.
We prefer an informal style but articles should be reasonably well written.
We almost always edit submitted material---sometimes quite considerably and sometimes without the author's intervention---for
the purpose of improving clarity and mathematical presentation.
It is appropriate to point out that contributions, possibly from authors whose first language is not English, will if necessary
be `cleaned up' to a high standard by our Editorial Board and volunteer proof-readers.
We are always especially interested in material that can be readily understood by first-year mathematics undergraduates.
A typical article on a mathematical topic would be 2--6 pages.
Longer articles are accepted at the Editor's discretion but usually limited to one per issue.
Please send items for publication to {\sf editor@m500.org.uk}.
To ensure items are processed promptly and to reduce the risk of loss,
names of files submitted {\em must consist only of letters, numbers and `-'}
% (in particular, do not use spaces or the underline symbol)
conforming to the pattern
$I$-$N$.$E$, where
$I$ is replaced by your initials,
$N$ is your choice of name (possibly with a suffix) for all the article's files, and
$.E$ is the extension.
For example, `IMV-3-Primes.tex', `IMV-3-Primes.pdf', `IMV-3-Primes-A.jpg', `IMV-3-Primes-B.jpg'.
The most important advice we can offer is:\ {\sc Please read recent issues of the magazine and please conform to its style}.
Please also note that {\sf M500} is printed on paper using only black ink and that the text block is only 115\,mm wide.
Plain English is preferred to mathematical jargon.
Avoid unreasonable use of symbols.
So write `for all positive integers $n$' rather than some diabolical expression like `$\forall n\in \mathbb{Z}^+$',
write `therefore' instead of `$\therefore$', etc.\ etc.
Do not start a sentence with a symbol, or a word like `calorie'.
Do not use theorems, pictures, diagrams, tables, etc.\ as nouns, and be aware that we might move such items from their original locations.
Try to avoid more than one level of subscripting or superscripting.
Generally, avoid any unnecessary reduction of type size; so $a/(2b)$ is better than $\frac{a}{2b}$, for instance.
% Avoid the usual amateurisms, such as inappropriate emphasis and excessive use of exclamation and question marks.
Avoid redundant brackets, non-standard fonts for variables and bizarre deviations from standard mathematical presentation.
Avoid excessive spoon-feeding.
\newpage
\noindent {\bf LaTeX}~ {\sf M500} is set using LaTeX, and therefore this is the preferred option for submitted material.
If you are interested in learning LaTeX, the Open University School of Mathematics and Statistics have produced some useful
resources to help OU students get started and which you can access by signing in to here using your Open University username and password:
{\small \url{https://learn2.open.ac.uk/course/view.php?id=206217&cmid=1172763}}.
Or you can find out everything you need to know from Wikipedia's {\em Guide to LaTeX}.
For those of you who are already set up to use LaTeX, the TeX file for these notes, available as
Sample LaTeX file in \url{m500.org.uk/magazine/},
is essentially the same as for the magazine itself and we suggest that you download it for your use.
Here are a few rules. Please comply with them.
Ensure there is extra space on both sides of the main symbol in displayed mathematics.
For example, write `\mfhtilde=\mfhtilde\ 1' rather than ` = 1' in
$$\cos^2\theta + \sin^2\theta ~=~ 1.$$
Ensure that mathematical items are properly separated. Remember that in math mode a comma is not followed by any space;
so, for example, write `\$a=1\$, \$b=2\$, \$c=3\$' rather than `\$a=1, b=2, c=3\$'.
Use `$\backslash$dfrac\{a\}\{2b\}' to get a full-size fraction $\dfrac{a}{2b}$ (rather than `\{a $\backslash$over 2b\}').
Use `$\backslash$dots' rather than `...'. Use `$\backslash$cdot' or `$\backslash$times' for explicit multiplication.
A decimal point is an ordinary full stop.
Remember to put a backslash after a full stop that is not the end of a sentence.
Reset the appropriate counters if you are automatically numbering equations, etc.
Also be aware that some LaTeX packages will clash with the ones that we use for {\sf M500}.
\mfhAdvGap
\noindent {\bf LyX}~ If you have never used LaTeX before, you could seriously consider using LyX instead.
LyX is a fully featured document processor with a mathematical formula editor which, it is claimed, is easily the best.
All the power of LaTeX is available.
But, and this is what might make the system attractive, you enter complicated mathematical equations easily by point-and-click from pop-up and drop-down menus.
Mathematical formul{\ae} are displayed on the screen as you enter them.
The main benefit, however, is that LyX can create LaTeX source code which I can copy and paste into {\sf M500}.
You need to send me the .tex and .pdf files, which you create by exporting your document as LaTeX (pdflatex) as well as PDF (pdflatex).
To find out more, go to \url{https://www.lyx.org/Home}.
\newpage
\begin{spacing}{0.96}
\noindent {\bf Other word processors}~ The existence of non-LaTeX word processors is an unfortunate complication because
I usually have to convert mathematical constructs by hand.
This might explain to some authors why their contributions get held up.
My recommendation would be to give up and go over to LaTeX.
From my own experience, once you have mastered the basic principles you will wonder why you
ever used anything else.
If you cannot create a LaTeX document, {\sc avoid symbols that are not in the set}
\begin{center}
\{., ,, ;, :, \textquotesingle, @, *, (, ), [, ], \{, \}, =, -, +, /, $<$, $>$, ?, !, \mfhcarrot, \underline{\;\;}\}.
\end{center}
This is important because symbols outside the set,
such as the minus sign, fancy quotes, Greek and other non-English letters,
need action by me---with the consequent likelihood of human error.
Always use \mfhcarrot\{\dots\} and \underline{\;\;}\{\dots\} to indicate superscripts and subscripts respectively;
so, for example, write
\begin{center}
x\underline{\;\;}\{1\}\mfhcarrot \{88\} + x\underline{\;\;}\{2\}\mfhcarrot \{99\}
\end{center}
if you want to see
\begin{center}
$x_1^{88} + x_2^{99}$.
\end{center}
Greek letters must be spelled out, capitalizing the first letter for the upper case versions;
\begin{center}
alpha, beta, gamma, Gamma, \dots, omega, Omega.
\end{center}
If you are using a {\sc Windows} computer, {use font {\sc Courier New} throughout} your entire document.
This helps with the conversion to LaTeX.
If you are using {\sc WORD}, the first thing to do is {\sc disable all AutoFormat options}.
And please
{\sc do not create mathematical objects with the equation editor}.
They might look pretty on your screen, but to me they are a nuisance because I would have to copy them entirely
by hand---with the inevitable introduction of errors. So, for example, write
\begin{center}
{sec\mfhcarrot 2 theta - tan\mfhcarrot 2 theta = 1}
\end{center}
instead of using the equation editor.
Even better, prepare your article as if you were doing it in LaTeX, so that the above would be written as
\begin{center}
\$\$ $\backslash$sec\mfhcarrot 2 $\backslash$theta - $\backslash$tan\mfhcarrot 2 $\backslash$theta \mfhtilde=\mfhtilde\ 1. \$\$
\end{center}
Fortunately, plain English requires little additional work and is very much preferred.
So, if you do not have LaTeX installed, please write mathematical stuff in English, as, for instance,
\begin{center}
integral from -infty to infty e\mfhcarrot\{-x\mfhcarrot 2\} dx = sqrt\{pi\},
\end{center}
corresponding to the LaTeX form,
\begin{center}
\$$\backslash$int\underline{\;\;}\{-$\backslash$infty\}\mfhcarrot\{$\backslash$infty\} e\mfhcarrot\{-x\mfhcarrot2\} dx
= $\backslash$sqrt\{$\backslash$pi\}\$,
\end{center}
which will appear as
$\int_{-\infty}^\infty e^{-x^2} dx = \sqrt{\pi}.$
With a little imagination and common sense you should be able to make yourself clear.
Remember to send me the PDF file of your article as well as the original word processor document.
If you cannot submit a LaTeX document and if you want prompt attention, please comply with the advice given in this section.
If you submit a large document where much of the text has to be entered by hand,
it might take a very long time for your article to appear in {\sf M500}.
\mfhAdvGap
\noindent {\bf Short contributions}~
The above rules really only apply to substantial articles involving many pages.
We also welcome contributions of more modest length, anything from few lines to a couple of pages.
Please feel free to send us mathematical notes, letters, experiences, reminiscences, anecdotes, etc.\ and hopefully we are not too fussy about how they arrive.
We are especially interested in mathematical problems and the solutions thereof.
And please note that there is no time limit for submitting an answer to a problem that has appeared in {\sf M500}.
\mfhAdvGap
\noindent {\bf Unwelcome material}~
Yes, we do seem to get our fair share of things that we cannot possibly use.
To give you some idea of the sort of stuff we will not accept, here is a short list:
(i) defamation of an identifiable living individual;
(ii) defamation of a named existing organization or any of its products or services;
(iii) material that the Editor would not wish his wife or his servants to see;
(iv) racism;
(v) blasphemy;
(vi) material that ridicules an {\sf M500} author other than the Editor;
(vii) solutions to Open University assignment questions;
(viii) notices for events due to occur before the magazine is likely to reach its readers;
(ix) material published elsewhere and protected by copyright, except under exceptional circumstances in which case the submitter must obtain permission;
(x) material that is blatantly erroneous;
(xi) material of an excessive length that cannot be justified for the nature of the subject-matter;
(xii) off-topic material of excessive length;
(xiii) excessively cranky treatments of standard mathematical topics;
(xiv) puerile material;
(xv) proofs of Fermat's Last Theorem.
\end{spacing}
\newpage
\noindent {\bf Personal information}~
If you choose to submit an article for {\sf M500}, the Editor will acquire
your name and at least one of your email and postal addresses.
This personal information, as well as any other personal information that you have chosen to provide within the body of your article, will be kept indefinitely on the Editor's computer system and its backups.
Your name and, if supplied, your email address will also be stored on computer systems operated by proofreaders to whom
the {\sf M500} issue containing your article is sent for examination.
The proofreaders for an {\sf M500} issue are drawn from, at the Editor's discretion,
members of the M500 Society Committee,
academic colleagues of the {\sf M500} Editor,
and authors, possibly including yourself, of substantial contributions to the same issue.
When your article is published your name
will appear as author of your article in the online version of {\sf M500} as well as
any online document, including the {\sf M500} Index, that cites, indexes or catalogues your work.
Any personal information of a descriptive nature that you have chosen to provide about yourself within the body of your article will also appear.
Personal information contained in an issue of {\sf M500} may be stored indefinitely in computer systems operated by the persons who acquire it.
For general information on how the M500 Society handles personal information, see \url{m500.org.uk/privacy/};
in cases of inconsistency {\em Advice for authors} shall prevail.
\mfhAdvGap
\noindent {\bf About {\sf M500}}~
The magazine {\sf M500} is published six times a year, with publication dates
28 February, 30 April, 30 June, 31 August, 31 October and 31 December.
Upon publication, an issue of {\sf M500} is distributed to all members of the M500 Society.
It may also be given to non-members at the discretion of the Editor or other M500 Society members.
Twelve months after publication an issue of {\sf M500} is placed on the M500 Society's web site at \url{m500.org.uk/magazine/}
for free browsing or downloading by anybody.
When an issue of {\sf M500} is uploaded to the M500 Society's web site we usually remove authors' personal identifiers other than names.
In particular, we remove private email and postal addresses.
Personal information of a descriptive nature will usually be retained.
Errors in the original published version may be corrected by us for the online version but, unless the error is obvious, we usually seek approval from the authors.
We will, usually without seeking approval, alter or remove material to which any of items (i)--(vi) and (ix) of Unwelcome material, above, might apply.
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