Challenge: sum of squares. Let's break 299

[peacecalc]

Hello folks,

I don't investigate very much time towards this problem. I beg your pardon if I wrote down a silly idea: If n = 299 then the biggest square number is 24^2 = (299 + 277), other possibilities (298 + 278) and so on. Maybe a initial program can generate all possible pairs of number which results in a square number.

Is known wether every square number from 1^2 .. 24^2 appears? The same square number can appear more then one time (can be seen in the examples) and it is logical, too. Because the numbers from 1 to 299 give 298 pairs of sum...