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IMO Shortlist 2012, Number Theory 8

Source: IMO Shortlist 2012, Number Theory 8

July 26, 2013
Gaussmodular arithmeticnumber theoryDivisibilityprimeIMO Shortlist

Problem Statement

Prove that for every prime p>100p>100 and every integer rr, there exist two integers aa and bb such that pp divides a2+b5āˆ’ra^2+b^5-r.
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