The famous Pythagorean theorem states that a right triangle, having side lengths A and B and hypotenuse length C, satisfies the formula
C2. It is also well known that there exist some right triangles in which all three side lengths are integral, such as the classic:
Further examples, both having A = 12, are the following:
The question is, given a fixed integer value for A, how many distinct integers B > A exist such that the hypotenuse length C is integral?
Each line contains a single integer A (2 ≤ A < 1048576 =
220). The end of the input is designated by a line containing the value 0.
For each value of A, output the number of integers B > A such that a right triangle having side lengths A and B has a hypotenuse with integral length.
3 12 2 1048574 1048575 0
1 2 0 1 175