Feit-Thompson conjecture

Statement
The conjecture states that if $$p,q$$ are distinct primes, then $$\Phi_p(q) = (q^p - 1)/(q - 1)$$ does not divide $$\Phi_q(p) = (p^q - 1)/(p-1)$$.

The stronger conjecture that $$\Phi_p(q)$$ and $$\Phi_q(p)$$ are relatively prime is false. The smallest counterexample is $$p = 17, q = 3313$$.

Related facts

 * Feit-Thompson theorem: The proof of the theorem by Feit and Thompson that every group of odd order is solvable can be simplified considerably if the Feit-Thompson conjecture is true.

Subject wiki links

 * Number:Feit-Thompson conjecture