# Feit-Thompson Conjecture

## Conjecture

There exist no distinct prime numbers $p$ and $q$ such that:

$\dfrac {p^q - 1} {p - 1}$ divides $\dfrac {q^p - 1} {q - 1}$

### Stronger Feit-Thompson Conjecture

There exist no distinct prime numbers $p$ and $q$ such that:

$\dfrac {p^q - 1} {p - 1}$ and $\dfrac {q^p - 1} {q - 1}$ are coprime.

## Source of Name

This entry was named for Walter Feit and John Griggs Thompson.