For what sequences of consecutive perfect squares would the sum be a perfect square?

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For example, the sum of the sequence of perfect squares from 1^2 to 24^2 = 70^2.

What other sequences (of let's say length >= 5) of some starting n^2 and ending m^2 would sum to a perfect square?

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This is a famous problem and the answer is none. The challenge is to prove it which isn't so hard once you know the answer ahead of time. Try it.