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| − | '''Euler's phi function''' determines the number of integers less than a given positive integer that are [[relatively prime]] to that integer.
| + | #REDIRECT [[Euler's totient function]] |
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| − | === Formulas ===
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| − | Given the [[prime factorization]] of <math>{n} = {p}_1^{e_1}{p}_2^{e_2} \cdots {p}_n^{e_n}</math>, then one formula for <math>\phi(n)</math> is <math> \phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right) \cdots \left(1-\frac{1}{p_n}\right) </math>.
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| − | === Identities ===
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| − | For [[prime]] p, <math>\phi(p)=p-1</math>, because all numbers less than <math>{p}</math> are relatively prime to it.
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| − | For relatively prime <math>{a}, {b}</math>, <math> \phi{(a)}\phi{(b)} = \phi{(ab)} </math>.
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| − | === Other Names ===
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| − | * Totient Function
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| − | * Euler's Totient Function
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