what is the smallest whole number that can be written two ways as a sum of two different perfect squares? i.e.11squared plus 3 squared is 121+ 9=130 and7 squared + 9squared=49 +81= 130. Are there any smaller? I am stumped!
Thanks !

Hi,

Just write down the squares up to 121:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121.

Then you look at a sum of two of them and see if you can get it as a sum of two others: 1+4 = 5 but you cannot get 5 in any other way.
1+9 = 10 but you cannot get 10 in any other way.
.
.
.
1+49 = 50 and you can get it as 25+25, but these are not two different perfect squares.
.
.
.
4+81=85 and 36+49=85. Is it the smallest?

Cheers,
Claude