Competition problem — Number theory

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Number theory Difficulty 5.7 AIME, harder Prove it

9. Show that if $a, b$ , and $c$ are integers with $c \mid a b$ , then $c \mid(a, c)(b, c)$ .

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.