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.

Posted by Ady TZIDON on 2012-11-09 02:27:27