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Finding x such that 3^n||x^3+17

Source: Japanese MO Finals 1999

February 11, 2011
number theory proposednumber theory

Problem Statement

Let f(x)=x3+17f(x)=x^3+17. Prove that for every integer n≥2n\ge 2 there exists a natural number xx for which f(x)f(x) is divisible by 3n3^n but not by 3n+13^{n+1}.
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