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In number theory, a branch of mathematics, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula: where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently-large odd number is the sum of three primes.

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• Ramanujan's sum
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• In number theory, a branch of mathematics, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula: where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently-large odd number is the sum of three primes.
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• In number theory, a branch of mathematics, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula: where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently-large odd number is the sum of three primes.
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