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On the Sum of the Reciprocals of the Fermat Numbers and Related Irrationalities

Published online by Cambridge University Press:  20 November 2018

Solomon W. Golomb
Solomon W. Golomb*
Affiliation:
California Institute of Technology
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In (1), P. Erdös showed that the function

takes on irrational values whenever z = 1/t, t = 2 , 3 , 4 , 5 , . . . . The method of proof uses Lambert's identity,

where d(n) is the number of divisors of n; and it is shown that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 475 - 478
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Erdös, P., On arithmetical properties of Lambert Series, J. Indian Math. Soc, 12 (1948), 63–66.Google Scholar