RO-NMO 2005 Problem 72

Let $a,b$ be two integers. Prove that

a) $13 \mid 2a+3b$ if and only if $13 \mid 2b-3a$ ; b) If $13 \mid a^2+b^2$ then $13 \mid (2a+3b)(2b+3a)$ .

Mircea Fianu

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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