IMO 1971 LL GBR14

Note that 83 −73 = 169 = 132 and 13 = 22 + 32. Prove that

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IMO 1971 LL GBR14

Origin: GBR

Problem

Note that 83 −73 = 169 = 132 and 13 = 22 + 32. Prove that if the difference between two consecutive cubes is a square, then it is the square of the sum of two consecutive squares.