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Divisors and Perfect Squares

Source: 2nd Final Mathematical Cup Junior Division P1 (2020)

October 1, 2020
number theoryDivisorsPerfect Squares

Problem Statement

Let nn be a given positive integer. Prove that there is no positive divisor dd of 2n22n^2 such that d2n2+d3d^2n^2+d^3 is a square of an integer.
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