5

Part of 1991 Mexico National Olympiad

Problems(1)

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

Source: Mexican Mathematical Olympiad 1991 OMM P5

The sum of squares of two consecutive integers can be a square, as in

3^2+4^2 =5^2

. Prove that the sum of squares of

m

consecutive integers cannot be a square for

m = 3

6

and find an example of

11

consecutive integers the sum of whose squares is a square.

consecutiveSum of Squaresnumber theory