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Sum of consecutive squares

Source: Irish MO

May 2, 2012
modular arithmeticDiophantine equationnumber theory unsolvednumber theory

Problem Statement

Problem. The sum of two consecutive squares can be a square; for instance 32+42=523^2 + 4^2 = 5^2.
(a) Prove that the sum of mm consecutive squares cannot be a square for māˆˆ{3,4,5,6}m \in \{3, 4, 5, 6\}. (b) Find an example of eleven consecutive squares whose sum is a square.
Can anyone help me with this? Thanks.
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