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x^3 - 17x^2 + ax - b^2 = 0 , 3 integer roots

Source: Austrian - Polish 1998 APMC

May 4, 2020
Integer PolynomialIntegerspolynomialalgebra

Problem Statement

Determine all pairs (a,b)(a, b) of positive integers for which the equation x3−17x2+ax−b2=0x^3 - 17x^2 + ax - b^2 = 0 has three integer roots (not necessarily different).
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