a, b, and x are positive integers such that

sqrt(a) + sqrt(b) = sqrt(x)

How many possible values of x less than or equal to 1000 are there?

If √a+√b=√x, then a+b+2√ab=x; we must have ab=L². In this case, a=L²/M and b=M.

We can try all possible (L,M) pairs such that L² can be divided by M, and L²/M+M+2L≤1000, or (L+M)²≤1000M.

Posted by Old Original Oskar! on 2005-05-05 19:56:06