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

re(2): Not proven yet but I have a guess by Charlie)

My second st6atement is totally wrong and out of place .On the contrary, **every prime number of the form 4k+1 CAN be expressed as the sum of 2 squares.**

I am going to erase this immediately.

RE 49. - 49=0+49 and zero is a valid integer and the statement holds.