Pythagoras's Revenge#10100
The famous Pythagorean theorem states that a right triangle, having side lengths and and hypotenuse length , satisfies the formula A^2 + B^2 = C^2. 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 , how many distinct integers B > A exist such that the hypotenuse length is integral?
Each line contains a single integer (2 \leq A < 1048576 = 2^{20}). The end of the input is designated by a line containing the value .
For each value of , output the number of integers B > A such that a right triangle having side lengths and has a hypotenuse with integral length.
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