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both roots of x^2+(2-3n^2)x+(n^2-1)^2=0 are perfect squares

Source: 2009 Belarus TST 4.1

November 8, 2020
Perfect SquaresPerfect Squarenumber theory

Problem Statement

Prove that there exist many natural numbers n so that both roots of the quadratic equation x2+(2−3n2)x+(n2−1)2=0x^2+(2-3n^2)x+(n^2-1)^2=0 are perfect squares.
S. Kuzmich
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