Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constructive Proof of Masser's Theorem   The Modified Szpiro Conjecture, equivalent to the $abc$ Conjecture, states
that for each $\epsilon>0$, there are finitely many rational elliptic curves
satisfying $N_{E}^{6+\epsilon}<\max\!\left\{ \left\vert
c_{4}^{3}\right\vert,c_{6}^{2}\right\} $ where $c_{4}$ and $c_{6}$ are the
invariants associated to a minimal model of $E$ and $N_{E}$ is the conductor of
$E$. We say $E$ is a good elliptic curve if $N_{E}^{6}<\max\!\left\{ \left\vert
c_{4}^{3}\right\vert,c_{6}^{2}\right\} $. Masser showed that there are
infinitely many good Frey curves. Here we give a constructive proof of this
assertion.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc