As 2015 is worth 7, mod 8, it cannot be expressible as the sum of 3 squares, each of which must be congruent to {0,1,4}, mod 8.
As 2015 is odd, one or all 3 squares must be odd:
Odd + odd + odd= 1+1+1 = 3 mod 8.
Odd + even + even = 1+0+0, 1+0+4, 1+4+4, mod 8; or {1,5} mod 8.

Posted by broll
on 20150708 12:04:49 