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In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as () or (), and may also be called Euler's phi function.
Euler totient phi function is used in modular arithmetic. It is used in Euler's theorem: If $ n $ is an integer superior or equal to 1 and $ a $ an integer coprime with $ n $, then $$ a^ {\varphi (n)} \equiv 1 \mod n $$ Example: $ n=7 $ , $ a=3 $ and $ \varphi (7) = 6 $ so $ 3^6 = 729 \equiv 1 \mod 7 $
24 kwi 2024 · Euler’s Totient function, also known as Euler's Phi Function Φ (n) is a mathematical function that counts the number of positive integers up to a given integer n that are relatively prime to n. i.e., the numbers whose GCD (Greatest Common Divisor) with n is 1.
20 mar 2022 · This function is usually called the Euler \(\phi\) function or the Euler totient function and has many connections to number theory. We won't focus on the number-theoretic aspects here, only being able to compute \(\phi(n)\) efficiently for any \(n\).
Funkcja φ (Eulera) lub tocjent – funkcja przypisująca każdej liczbie naturalnej liczbę liczb względnie pierwszych z nią i nie większych od niej [1]. Nazwa pochodzi od nazwiska Leonharda Eulera [a] [2] [3] [4] [5]. Kilka początkowych wartości funkcji. Funkcja Eulera odgrywa dużą rolę w teorii liczb.
Euler's totient function (also called the Phi function) counts the number of positive integers less than \(n\) that are coprime to \(n\). That is, \(\phi(n)\) is the number of \(m\in\mathbb{N}\) such that \(1\le m \lt n\) and \(\gcd(m,n)=1\).
The totient function phi (n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any factor in common with) n, where 1 is counted as being relatively prime to all numbers.
