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integer P(x) = n has m roots (V Soros Olympiad 1998-99 Round 1 11.7)

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May 25, 2024
algebrapolynomial

Problem Statement

For what is the smallest natural number nn there is a polynomial P(x)P(x) with integer coefficients, having mm different integer roots, and at the same time the equation P(x)=nP(x) = n has at least one integer solution if: a) m=5m = 5, b) m=6 m = 6?
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