Definition: Euler function

The Euler function $\phi:\mathbb N\to\mathbb N$ is an arithmetic function $\phi(n)$ counts how many numbers in the subset of natural numbers $\{1,2,\ldots,n\}$ are co-prime to $n.$


The $\phi$ function was first described by Leonhard Euler (1707 - 1783). It can be visualized using SageMath. If you click on the evaluate button, you will see the values of $\tau(n)$ for $n=1,\ldots,100.$

phipoints= [(i, euler_phi(i)) for i in range(1,100)] list_plot(phipoints)

Definitions: 1
Examples: 2
Proofs: 3 4 5
Propositions: 6 7
Sections: 8
Theorems: 9

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  1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
  2. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927