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n^2 + d not a square if d divides 2n^2

Source: 1953 Hungary - Kürschák Competition p2

October 10, 2022
number theoryPerfect Squaredivides

Problem Statement

nn and dd are positive integers such that dd divides 2n22n^2. Prove that n2+dn^2 + d cannot be a square.
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