Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary recurrences, Jacobi symbol criterion, Integer points on elliptic
  curves   In 1987, Ming Luo showed that the Fibonacci number $U_n$ is Triangular if and
only if $n=\pm1,2,4,8,10$. For this, he established a Jacobi Symbol Criterion.
Moreover, he observed this problem is equivalent to finding all integer points
on two elliptic curves. In this paper, we prove a Jacobi Symbol Criterion for
more general families of binary recurrences. In addition, applying the
criterion, we determine all integer points on the elliptic curves
$y^2=5x^2(x+3)^2+4(-1)^n$.

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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ph