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Largest 'Olympic' number not exceeding 2015

Source: St. Petersburg Math Olympiad, 2015, round ii, grade 10, P4

September 30, 2016
number theoryquadratics

Problem Statement

A positive integer nn is called Olympic, if there exists a quadratic trinomial with integer coeffecients f(x)f(x) satisfying f(f(n))=0f(f(\sqrt{n}))=0. Determine, with proof, the largest Olympic number not exceeding 20152015.
A. Khrabrov
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