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x^2 - rx- 1

Source: Polish MO Finals 1974 p3

August 23, 2024
algebrapolynomialquadratic polynomial

Problem Statement

Let rr be a natural number. Prove that the quadratic trinomial x2−rx−1x^2 - rx- 1 does not divide any nonzero polynomial whose coefficients are integers with absolute values less than rr.
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