Let P(x) be a polynomial with integer coefficients of degree d>0.
- If α and β are two integers such that P(α)=1 and P(β)=−1, then prove that |β−α| divides 2.
- Prove that the number of distinct integer roots of (P(x))2−1 is at most d+2.
First one is very easy. But I cannot understand how to prove the second one. I would appreciate any help.
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