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That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.
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http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html
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Abc Conjecture
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Beal Conjecture
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K-tuple Conjecture
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Wild Conjecture
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The Union Of Uniform Closed Balls Conjecture
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