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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 $n.$

Example.

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)

| | | | | created: 2019-03-21 06:59:01 | modified: 2019-05-15 19:57:10 | by: bookofproofs | references: [701], [1272]


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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

[701] Scheid Harald: “Zahlentheorie”, Spektrum Akademischer Verlag, 2003, 3. Auflage

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