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The general formula for Euler's totient function is $\varphi(n) = n \prod_{i=1}^{m} \left(1 - \frac{1}{p_i}\right)$, where $p_1, p_2, \ldots, p_m$ are the distinct prime factors of $n$. This formula is derived by combining the multiplicativity of $\varphi$, the prime power formula $\varphi(p^k) = p^k - p^{k-1}$, and the Fundamental Theorem of Arithmetic.

Conditions: $n$ is a positive integer greater than 1.; $p_1, \ldots, p_m$ are all the distinct prime factors of $n$.

The general formula for Euler's totient function is $\varphi(n) = n \prod_{i=1}^{m} \left(1 - \frac{1}{p_i}\right)$, where $p_1, p_2, \ldots, p_m$ are the distinct prime factors of $n$. This formula is derived by combining the multiplicativity of $\varphi$, the prime power formula $\varphi(p^k) = p^k - p^{k-1}$, and the Fundamental Theorem of Arithmetic.

Conditions: $n$ is a positive integer greater than 1.; $p_1, \ldots, p_m$ are all the distinct prime factors of $n$.

Euler's totient function $\varphi(n)$ is defined as the number of integers from 1 to $n$ that are coprime to $n$. Two integers are coprime if their greatest common divisor is 1.

Conditions: $n$ is a positive integer.; The counting range is from 1 to $n$ inclusive.; Coprimality is determined by the greatest common divisor being 1.

Euler's totient function $\varphi(n)$ is defined as the number of integers from 1 to $n$ that are coprime to $n$. Two integers are coprime if their greatest common divisor is 1.

Conditions: $n$ is a positive integer.; The counting range is from 1 to $n$ inclusive.; Coprimality is determined by the greatest common divisor being 1.