It is, of course, quite possible for two consecutive numbers both to be the sum of two squares; for example 17=4^2+1^2, and 18=3^2+3^2.

Now although x is not itself a sum of 2 positive squares, each of x-3,x-2,x-1,x+1,x+2 and x+5 is a sum of two positive squares, say a^2, b^2, c^2...etc. such that 8 of the numbers a,b,c...etc. form consecutive members of an arithmetic sequence.

What is x?

(In reply to Computer Search (spoiler) by Harry)

Correct, compare the list table of n,a(n) for n=1 to 10000 in A000404 in Sloane.

Posted by broll on 2011-10-18 22:44:53