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TOT 345 1992 Autumn A J3 (P-Q)(x), P(x), (P+Q)(x) re squares of polynomials

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June 10, 2024
algebrapolynomial

Problem Statement

Do there exist two polynomials P(x)P(x) and Q(x)Q(x) with integer coefficients such that (P−Q)(x),    P(x)    and    (P+Q)(x)(P-Q)(x), \,\,\,\, P(x) \,\,\,\, and \,\,\,\,(P+Q)(x) are squares of polynomials (and QQ is not equal to cPcP, where cc is a real number)?
(V Prasolov)
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