Abstract:
Let n, x, y, z be any given integers. The study of n for which n = x
2 + y
2 + z
2
is a very long
standing problem. Recent survey of sizeable literature shows that many researchers have made some
progress to come up with algorithms of decomposing integers into sums of three squares. On the
other hand, available results on integer representation as sums of three square is still very minimal.
If a, b, c, d, k, m, n, u, v and w are any non-negative integers, this study determines the sum of three
square formula of the form abcd+ka2 +ma+n = u
2 +v
2 +w
2 and establishes its applications to various
cases
