Hint to puzzle 159: Eight odd squares
By Lagrange's Theorem, for any non-negative integer n we have n = a2 + b2 + c2 + d2, where a, b, c, and d are non-negative integers.
Now consider that 8a2 = (4a2 + 4a) + (4a2 − 4a).
By Lagrange's Theorem, for any non-negative integer n we have n = a2 + b2 + c2 + d2, where a, b, c, and d are non-negative integers.
Now consider that 8a2 = (4a2 + 4a) + (4a2 − 4a).