Competition problem — Number theory

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Number theory Difficulty 5.8 AIME, harder Prove it

6. Show that if $a, b, c$ , and $m$ are integers such that $c>0, m>0$ , and $a \equiv b(\bmod m)$ , then $a c \equiv b c(\bmod m c)$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.