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Algebra Level 4

Suppose f(x)f(x) is a monic integer polynomial of degree three. Find the largest possible number of distinct integers nn such that f(n2)=f(n)f(n^2)=f(n).

Details and assumptions

A polynomial is monic if its leading coefficient is 1. For example, the polynomial x3+3x5 x^3 + 3x - 5 is monic but the polynomial x4+2x36 -x^4 + 2x^3 - 6 is not.

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