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  "body": "\n## Statement\n\nLet $n \\ge 2$ be an integer. Suppose that $p_1, \\dots, p_m$ are the distinct [[prime numbers|0SN0MAEKYX]] that divide $n$.\nThen\n$$\\varphi(n) = n \\prod_{i=1}^{m} \\frac{p_i - 1}{p_i},$$\nwhere $\\varphi$ is [[Euler's totient function|0VV04M41AN]].\n\n## Remarks\n\nEach factor equals $1 - 1/p_i$, so only the set of primes dividing $n$ matters, not their exponents.\nFor example, $12 = 2^2 \\cdot 3$ gives $\\varphi(12) = 12 \\cdot \\frac{1}{2} \\cdot \\frac{2}{3} = 4$.\n",
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