A Golden Pair of Identities in the Theory of Numbers

Details A Golden Pair of Identities in the Theory of Numbers A Golden Pair of Identities in the Theory of Numbers

2011-09-14

arxiv.org/abs/1109.3216v2

Mathematics

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Scientific paper

We find an interesting relationship between the golden ratio, the Moebius function, the Euler totient function and the natural logarithm - central players in the theory of numbers. A number of identities involving the golden ratio and its reciprocal are proved, including an expression for the base of the natural logarithm. The theorem and corollaries highlight a connection between the golden ratio and the factorization of integers that is not obvious; and display a sort of inverse relationship between the Moebius function and Euler totient function.

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