Feit-Thompson Conjecture/Stronger/Mistake/First Edition

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$17$

Mistake

The only known prime values for which $p^q - 1$ and $q^p - 1$ have a common factor less than $400,000$ are $17$ and $3313$. The common factor is $112,643$.

Correction

The correct expressions are $\dfrac {p^q - 1} {p - 1}$ and $\dfrac {q^p - 1} {q - 1}$.

It appears that the author misrepresented the refutation of the 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 not coprime.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $17$