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==Definition==
 
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*<math>n\equiv a\pmod{b}</math> if <math>n</math> is the remainder when <math>a</math> is divided by <math>b</math> to give an integral amount.
 
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Revision as of 18:54, 3 October 2007



The Problem Solver's Resource
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 6.

Modulos

Definition

  • $n\equiv a\pmod{b}$ if $n$ is the remainder when $a$ is divided by $b$ to give an integral amount.

Special Notation

Properties

For any number there will be only one congruent number modulo $m$ between $0$ and $m-1$.

If $a\equiv b \pmod{m}$ and $c \equiv d \pmod{m}$, then $(a+c) \equiv (b+d) \pmod {m}$.


$a \pmod{m} + b \pmod{m} \equiv (a + b) \pmod{m}$ $a \pmod{m} - b \pmod{m} \equiv (a - b) \pmod{m}$ $a \pmod{m} \cdot b \pmod{m} \equiv (a \cdot b) \pmod{m}$

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