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diff --git a/00_xxx/00038_Theory/00010_Totient-Function/index.md b/00_xxx/00038_Theory/00010_Totient-Function/index.md new file mode 100644 index 0000000..eea75f4 --- /dev/null +++ b/00_xxx/00038_Theory/00010_Totient-Function/index.md @@ -0,0 +1,16 @@ +# Euler's totient function + +And now something completely different. Straight from the World of Number Theory. +Frankly, I just wanted to show off the powers of my new Estatico functionality +and give tribute to my all time hero **Leonhard Euler**. + +## Definition + +For a given value _n_ this function returns the number of positive integers, +relatively prime to _n_ up to _n_. + +## Computing + +You can compute it for instance via _Euler's product formula_, multiplying +over the distinct prime numbers dividing _p_: +$$\varphi(n) =n \prod_{p\mid n} \left(1-\frac{1}{p}\right)$$ diff --git a/00_xxx/00038_Theory/index.md b/00_xxx/00038_Theory/index.md new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/00_xxx/00038_Theory/index.md |