Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary Quadratic Forms and Counterexamples to Hasse's Local-Global
  Principle   After a brief introduction to the classical theory of binary quadratic forms
we use these results for proving (most of) the claims made by P\'epin in a
series of articles on unsolvable quartic diophantine equations, and for
constructing families of counterexamples to the Hasse Principle for curves of
genus 1 defined by equations of the form $ax^4 + by^4 = z^2$.

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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: physics
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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: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin