A sum of three squares can be made to be a square. e.g.,
12 + 22 + 22 = 32
22 + 32 + 62 = 72
32 + 42 + 122 = 132
42 + 52 + 202 = 212
52 + 62 + 302 = 312
62 + 72 + 422 = 432
In general (1+n)2
+ (2+n)2 + (1+n)2(2+n)2 = [(n+1)(n+2) +1]2
It is found that (1+n)4 + (2+n)4 +
(1+n)2(2+n)4 is divisible by (n+1)(n+2) + 1
14 + 24 + 24 = 33 = 3 x 11
24 + 34
+ 64 = 1393 = 7 x 199
34 +
44 + 124 = 21073 = 13(1621)
44 + 54 + 204 = 160881 =
21(7661)
