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(2n+1)^3-2 is sum of 3n-1 perfect squares

Source: 2001 Cuba MO 1.3

September 15, 2024
number theoryPerfect Squares

Problem Statement

Let nn be a positive integer. a) Prove that the number (2n+1)3−(2n−1)3(2n + 1)^3 - (2n - 1)^3 is the sum of three perfect squares. b) Prove that the number (2n+1)3−2(2n+1)^3-2 is the sum of 3n−13n-1 perfect squares greater than 11.
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