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11 consecutive integers the sum of whose squares is a square.

Source: Mexican Mathematical Olympiad 1991 OMM P5

July 29, 2018
consecutiveSum of Squaresnumber theory

Problem Statement

The sum of squares of two consecutive integers can be a square, as in 32+42=523^2+4^2 =5^2. Prove that the sum of squares of mm consecutive integers cannot be a square for m=3m = 3 or 66 and find an example of 1111 consecutive integers the sum of whose squares is a square.
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