Euler's totient function
Carmichael's conjecture

This states that there is no number n with the property that for all other numbers m, m ≠ n, φ (m) ≠ φ (n). See 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.
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