Editing Euler's totient function (section)

===Carmichael's conjecture===

{{main article|Carmichael's totient function conjecture}}

This states that there is no number {{mvar|n}} with the property that for all other numbers {{mvar|m}}, {{math|''m'' ≠ ''n''}}, {{math|''φ''(''m'') ≠ ''φ''(''n'')}}. See [[#Ford's theorem|Ford's theorem]] above.

As stated in the main article, if there is a single counterexample to this conjecture, there must be infinitely many counterexamples, and the smallest one has at least ten billion digits in base 10.<ref name=Guy144/>