Abstract
This short chapter introduces an important class of functions, called arithmetic multiplicative functions, which play a prominent role in the elementary theory of numbers. Among the many arithmetic multiplicative functions we shall encounter here, two deserve all spotlights: the Euler function φ, which will reveal itself to be an indispensable tool for basically all further theoretical developments, and the Möbius function μ, which is essential to getting the celebrated Möbius inversion formula and its subsequent application to the Euler function.
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Notes
- 1.
After the German mathematician of the nineteenth century August Möbius.
- 2.
Another approach was the object of Problem 6, page 40.
- 3.
Up to this day, no one knows whether or not there exist odd perfect numbers.
- 4.
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Caminha Muniz Neto, A. (2018). Arithmetic Functions. In: An Excursion through Elementary Mathematics, Volume III. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77977-5_8
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DOI: https://doi.org/10.1007/978-3-319-77977-5_8
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