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a number theory problem that makes you want to count

Source: Iranian RMM TST 2020 Day1 P1

January 14, 2020
number theoryprime numbers

Problem Statement

For all prime p>3p>3 with reminder 11 or 33 modulo 88 prove that the number triples (a,b,c),p=a2+bc,0<b<c<p(a,b,c), p=a^2+bc, 0<b<c<\sqrt{p} is odd.
Proposed by Navid Safaie
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