Each of the n consecutive positive integers x+1, x+2, ...., x+n is expressible as the sum of squares of two distinct positive integers.

Determine the maximum value of n and prove that no higher value of n is possible.

(In reply to

Not proven yet but I have a guess by Jer)

Assuming that no two consecutive odd numbers are the sum of two distinct positive integers==> than 3 is the limit, i.e. even number S, THEN ODD S+1, then even again s+2.

To show that such a triple exist , show an example :

e.g. **800 (=400+400), 801 (=576+225), 802 (=441+361), **