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169 divides 21n^2 + 89n + 44 if 13 divides n^2 + 3n + 51

Source: CRMO 2012 region 5 p2 Mumbai

September 30, 2018
number theoryDivisibilitydividesdivisor

Problem Statement

Prove that for all positive integers nn, 169169 divides 21n2+89n+4421n^2 + 89n + 44 if 1313 divides n2+3n+51n^2 + 3n + 51.
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