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(x^2 - px+q)(x^2 -qx+ p) has pos. integer roots

Source: 1984 Swedish Mathematical Competition p4

March 28, 2021
algebrapolynomial

Problem Statement

Find all positive integers pp and qq such that all the roots of the polynomial (x2−px+q)(x2−qx+p)(x^2 - px+q)(x^2 -qx+ p) are positive integers.
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