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Let f ∈ Z[x] be a nonconstant polynomial with the property that all the roots (in...

Let f ∈ Z[x] be a nonconstant polynomial with the property that all the roots (in comlex plane) for the equation f(x) = 0 are distinct. Prove that there exist infinitely many positive integers n such that f(n) is not a perfect square. Could you explain it in number theory instead of some deep math like sigel theorem

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