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AFAIK this problem was on a math competition this year, I was just wondering around how to solve it. I didn't know a formula for solving it, and what I did

was: I tried to square all numbers from 18 to n until I find some solutions that would satisfy an equation. I found 18 and 7, however there were 3 right solutions for this and I think that one of them was above 100 (x or y equals 100<), of course it's a little crazy to count all of them in 10 minutes, so I asked my math teacher for some clues, and he gave me one:

x^2-y^2=275 = (x-y)(x+y)=275

Now it look much simplier for me, but again I can't make anything useful out of it, in my point of view we must try to count the solutions in the same way as I did before without knowing teacher's clue. And here is my question:

Can anyone give me another important clue or try to explain that one above?

Also if you can, may I have some tutorials or "keywords" for google on those kind of problems?, I don't really know what to search if branch of math. is unknown to me. At last if you know any faster solutions where answer comes out in matter of minutes, aprox. - 2-5 minutes, can you write something about it?

Thank you all.

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# X^2-y^2=275 (find all solutions for x & y)

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