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Arithmetic Functions

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Topics in the Theory of Numbers

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

Earlier, we encountered the function τ(n), which gives the number of (positive) divisors of the number n, and we also met Euler’s function ϕ(n). Given the canonical decomposition of n we gave formulas to compute these functions. We also learned some interesting properties of Euler’s function. Al-though the function π(x), which gives the number of primes not exceeding x, is defined for all positive values x, its value can change only at integer values of the argument. Therefore, π(x) can also be viewed as a function whose domain consists of the positive integers.

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References

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Authors and Affiliations

  1. Department of Algebra and Number Theory, Eõtvõs Loránd University, Pázmány Péter Sétany 1/C, Budapest, H-1117, Hungary

    János Surányi

Authors
  1. Paul Erdős
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  2. János Surányi
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Erdős, P., Surányi, J. (2003). Arithmetic Functions. In: Topics in the Theory of Numbers. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0015-1_8

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  • DOI: https://doi.org/10.1007/978-1-4613-0015-1_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6545-0

  • Online ISBN: 978-1-4613-0015-1

  • eBook Packages: Springer Book Archive

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