Btukfyl

There are several nice answers using different packages. I'd like to note that TeX uses integer arithmetics, so it is easy to program the standard formula a-(a/b)*b, where / means integer division.

Plain TeX solution:

newcounttmpcnta

defmodulo#1#2{tmpcnta=#1

        dividetmpcnta by #2

        multiplytmpcnta by #2

        multiplytmpcnta by -1

        advancetmpcnta by #1relax

        thetmpcnta}

modulo{17}{3}

modulo{19}{3}

bye

LaTeX solution:

documentclass{article} 

makeatletter

newcommandmodulo[2]{@tempcnta=#1

        divide@tempcnta by #2

        multiply@tempcnta by #2

        multiply@tempcnta by -1

        advance@tempcnta by #1relax

        the@tempcnta}

makeatother

begin{document} 

modulo{17}{3}

modulo{19}{3}

end{document}

The fp package is small and provides the functionality to do quite complex arithmetic. In the minimal example below the macro modulo{<a>}{<b>} stores the result of <a> mod <b> in the macro result, which is then directly printed:

documentclass{article}

usepackage[nomessages]{fp}% http://ctan.org/pkg/fp

newcommand{modulo}[2]{%

  FPeval{result}{trunc(#1-(#2*trunc(#1/#2,0)),0)}result%

}

begin{document}

Some modular arithmetic:

begin{itemize}

  item $512 pmod{7}=modulo{512}{7}$

  item $6 pmod{4}=modulo{6}{4}$

  item $15 pmod{4}=modulo{15}{4}$

  item $1234567 pmod{3}=modulo{1234567}{3}$

end{itemize}

end{document}

Since the result is stored in result, it can be used later in the text as well, until another execution of modulo will overwrite result.

Similar functionality in terms of mathematical functions is provided with pgf as well.

The "expandable" version, using e-TeX's numexpr:

deftruncdiv#1#2{((#1-(#2-1)/2)/#2)}

defmoduloop#1#2{(#1-truncdiv{#1}{#2}*#2)}

defmodulo#1#2{numbernumexprmoduloop{#1}{#2}relax}

truncdiv and moduloop can be plugged into other expressions. It's necessary to do like this because numexpr performs rounded integer division.

Another solution is to use pgfmath

documentclass{article} 

input{pgfutil-common.tex}

usepackage{pgfkeys,pgfmath}

begin{document}



pgfmathparse{mod(20,6)} pgfmathresult %displays 2.0

pgfmathtruncatemacro{myint}{ pgfmathresult}  



myint %displays 2 

end{document}  

LaTeX3 (the expl3 package) also has a facility for computing modulus (moduli?), namely int_mod:nn.

documentclass{article}

usepackage{expl3}

ExplSyntaxOn

newcommand{mymod}[2]{int_mod:nn{#1}{#2}}

ExplSyntaxOff

begin{document}

  The residue of $45$ modulo $19$ is $mymod{45}{19}$.

end{document}

You can use the calculator package then, type this code:

MODULO{14}{3}{sol}



$14pmod{3}=sol$

You may use calc package as long as the absolute values of the numbers are not exceeding 2^31-1=2147483647. Otherwise you may use bigintcalc package.

documentclass{article}

usepackage{amsmath}

usepackage{calc}

newcounter{modulo}

newcommandmodulo[2]{%

  setcounter{modulo}{#1-(#1/#2)*#2}%

  arabic{modulo}%

}

begin{document}

begin{align*}

131 equiv modulo{131}{3} &pmod{3} \

131 equiv modulo{131}{5} &pmod{5} \

131 equiv modulo{131}{7} &pmod{7} \

131 equiv modulo{131}{8} &pmod{8} \

-97 equiv modulo{-97}{3} &pmod{3} \

-97 equiv modulo{-97}{5} &pmod{5} \

-97 equiv modulo{-97}{7} &pmod{7} \

-97 equiv modulo{-97}{8} &pmod{8} \

end{align*}

end{document}