Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Quadratic Formula Modulo N   Let $a, b, c,$ and $n$ be integers, with $a$ nonzero and $n$ at least two.
Necessary and sufficient conditions on these parameters are derived which
guarantee that all solutions of the congruence \[ ax^2+bx+c \equiv 0\
\textrm{mod}\ n \] are given precisely by the solutions of \[ 2ax\equiv -b+s \
\textrm{mod}\ n, \] where $s$ varies over all solutions of \[ x^2\equiv b^2-4ac
\ \textrm{mod}\ n. \] Corollaries of this result are deduced for prime-power
moduli and some illustrative examples are also presented.

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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat