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integer trinomial as a perfect square

Source: Czech-Polish-Slovak Match 2013 day 2 P1

September 29, 2017
Perfect Squaretrinomialnumber theoryInteger Polynomial

Problem Statement

Let aa and bb be integers, where bb is not a perfect square. Prove that x2+ax+bx^2 + ax + b may be the square of an integer only for finite number of integer values of xx.
(Martin Panák)
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