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In mathematics, '''Carmichael's totient function conjecture''' concerns the [[Multiplicity (mathematics)|multiplicity]] of values of [[Euler's totient function]] ''φ''(''n''), which counts the number of integers less than and [[coprime]] to ''n''. It states that, for every ''n'' there is at least one other integer ''m'' ≠ ''n'' such that ''φ''(''m'') = ''φ''(''n'').
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* {{citation |last=Guy | first=Richard K. | authorlink=Richard K. Guy | title=Unsolved problems in number theory | publisher=[[Springer-Verlag]] |edition=3rd | year=2004 |isbn=978-0-387-20860-2 | zbl=1058.11001 | at=B39 }}.
*{{citation
| last = Klee | first = V. L.
| doi = 10.1090/S0002-9904-1947-08940-0
| journal = [[Bulletin of the American Mathematical Society]]
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==External links==
*{{mathworld|title=Carmichael's Totient Function Conjecture|urlname=CarmichaelsTotientFunctionConjecture|mode=cs2}}
[[Category:Multiplicative functions]]
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