Feit-Thompson Conjecture/Stronger/Historical Note
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Historical Note on Stronger Feit-Thompson Conjecture
The stronger form of the Feit-Thompson Conjecture was refuted by Nelson Malcolm Stephens in $1971$, by means of a computer search.
Note that David Wells, in his Curious and Interesting Numbers of $1986$, misreports this result, stating it about the common divisor of $p^q - 1$ and $q^p - 1$.
Then in his Curious and Interesting Numbers, 2nd ed. of $1997$, he misreports this result again, in a different way, stating it about the common divisor of $p^p - 1$ and $q^q - 1$.
The latter is obviously spurious, as, given odd primes $p$ and $q$, $p^p - 1$ and $q^q - 1$ are both even, and hence have a common divisor of $2$.