In mathematics, Carmichael's Totient Function Conjecture concerns the multiplicity of values of Euler's totient function φ(n), the function which counts the number of integers less than and coprime to n.
This function φ(n) is equal to 2 when n is one of the three values 3, 4, and 6. It is equal to 4 when n is one of the four values 5, 8, 10, and 12. It is equal to 6 when n is one of the four values 7, 9, 14, and 18. In each case, there is more than one value of n having the same value of φ(n).
The conjecture asserts that this phenomenon of repeated values holds for every n. That is, for every n there is at least one other integer m ≠ n such that φ(m) = φ(n).
References
- Weisstein, Eric W. "Carmichael's Totient Function Conjecture." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CarmichaelsTotientFunctionConjecture.html
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