# Nice to square you

Algebra Level 4

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

Details and assumptions

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

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