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Analytic number theory
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Computational number theory
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Elementary number theory
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Irrationality and transcendence
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Bounding the sum by an integral
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Computational number theory front page
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Irrationality and transcendence front page
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Partial summation
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To establish that n is composite, show that Fermat's little theorem does not hold for n
To factorize n, find a non-trivial square root of 1 mod n
To find a factor of n, find some m such that (m,n) is not 1
To find a rational with low denominator near a given real, use continued fractions
To prove that a number is irrational, show that it is almost rational
To work out powers mod n, use repeated squaring
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