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Hi Would you please advise me? Consider the equation below: $$ ax^2+bxy+cy^2=n $$ in which $a, b, c$ and $n$ are integers. We then suppose that $a, b, c$ are constant. Is there any way to find the number of answers for the equation? Actually, I have already solved this equation for many different $a, b, c$ and the number of answers. And currently I'm looking for unsolved cases. By special thanks

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    @user11301 Much is known about this. Start [here](http://www.numbertheory.org/php/binary.html) and see the links. Also try [here](http://www.alpertron.com.ar/METHODS.HTM)2011-05-24
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    @user11301: One more [here](http://www.numbertheory.org/pdfs/binary.pdf)2011-05-24
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    The left part of your equation is what mathematicians call a (integral) quadratic form. There is a lot of results about the integers n they can represent or not.2011-05-24
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    I edited the title of your question to make it a tiny little bit more descriptive and a lot less urgent. I hope you're OK with that...2011-05-24
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    Try $$ x^2 + 11 y^2 = n.$$2011-05-25
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    Possible duplicate of [Counting the Number of Integral Solutions to $x^2+dy^2 = n$](https://math.stackexchange.com/questions/645171/counting-the-number-of-integral-solutions-to-x2dy2-n)2017-09-16

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