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From Pythagoras to …
Mathematics is beautiful, isn’t it? Well, I’m sure you all know the famous Pythagorean theorem. He found an amazing fact about triangles, that is if the triangle has a right angle, the following relation holds:
a2 + b2 = c2, where c is the length of the hypotenuse.
However, Pythagoras told us nothing more about the generalization below:
x2 + y2 = n, where n is an integer.
It is a natural tendency for mathematicians to solve whether an equation has integer solutions or not. But for you, a future computer scientist, will you also try to do some of the mathematicians’ work?
To simplify this problem, you are only required to find out whether the above equation x2 + y2 = n has integer solutions.
The first line of the input is an integer T (T ≤ 50), and the following T lines have an integer n each. It is guaranteed that each n fits in signed 64-bit integer type.
For each test case output “
POJ Monthly--2007.03.04, Ikki
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