Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$   It is a generalization of Pell's equation $x^2-Dy^2=0$. Here, we show that:
if our Diophantine equation has a particular integer solution and $ab$ is not a
perfect square, then the equation has an infinite number of solutions; in this
case we find a close expression for $(x_n,y_n)$, the general positive integer
solution, by an original method. More, we generalize it for any Diophantine
equation of second degree and with two unknowns $f(x,y)=0$.

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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph