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Polynomial with integer coefficients

Source: TST 2014 of Tajikistan

May 20, 2014
algebrapolynomialalgebra proposed

Problem Statement

Given the polynomial p(x)=x2+xāˆ’70p(x) = x^2 + x - 70, do there exist integers 0<m<n0<m<n, so that p(m)p(m) is divisible by nn and p(m+1)p(m+1) is divisible by n+1n+1?
Proposed by Nairy Sedrakyan
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