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Square Sum Sequences
We consider all sequences of 2m+1 consecutive integers with the special property that the sum of the squares of the first m + 1 numbers is equal to the sum of the squares of the last m numbers.
The first such sequence occurs for m = 1, in the sequence {3, 4, 5}, since: 3^2+4^2=5^2.
Challenger
Give the first number of the next sequence that satisfies this special property.
Mastermind
How many positive integers <= 2025 are part of such a sequence?