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?
(In reply to
re(3): First thoughts... ...(spoiler?) by Charlie)
To see why the numbers need not be perfect squares:
sqrt(a) + sqrt(b) = sqrt(x)
squaring:
a + b + 2*sqrt(a*b) = x
Only a*b need be a perfect square, so any prime factors that they have in common will form a perfect square and only the prime factors that they do not share need to be present in the original a and b in even powers.

Posted by Charlie
on 20050505 19:51:17 