What would you like to understand?

For a prime number $p$, the only positive divisors are 1 and $p$ itself. Any integer $a$ in the range from 1 to $p$ that is not equal to $p$ will not share the factor $p$.

Conditions: $p$ is a prime number.; $\varphi(p)$ is defined as the count of integers from 1 to $p$ that are coprime to $p$.

For a prime number $p$, the only positive divisors are 1 and $p$ itself. Any integer $a$ in the range from 1 to $p$ that is not equal to $p$ will not share the factor $p$.

Conditions: $p$ is a prime number.; $\varphi(p)$ is defined as the count of integers from 1 to $p$ that are coprime to $p$.

Euler's totient function is multiplicative, meaning $\varphi(nm) = \varphi(n)\varphi(m)$ whenever $\gcd(n, m) = 1$. In the prime factorization of $n$, the factors $p_i^{k_i}$ are powers of distinct primes.

Conditions: $n = p_1^{k_1}p_2^{k_2}\cdots p_m^{k_m}$ is the prime factorization of $n$.; $p_i$ are distinct prime numbers.; $\varphi$ is multiplicative for coprime integers.

Euler's totient function is multiplicative, meaning $\varphi(nm) = \varphi(n)\varphi(m)$ whenever $\gcd(n, m) = 1$. In the prime factorization of $n$, the factors $p_i^{k_i}$ are powers of distinct primes.

Conditions: $n = p_1^{k_1}p_2^{k_2}\cdots p_m^{k_m}$ is the prime factorization of $n$.; $p_i$ are distinct prime numbers.; $\varphi$ is multiplicative for coprime integers.