4.65 (1973)

Conjecture: $\frac{p^q - 1}{p - 1}$ never divides $\frac{q^p - 1}{q - 1}$ if $p, q$ are distinct primes. The validity of this conjecture would simplify the proof of solvability of groups of odd order (W. Feit, J. G. Thompson, Pacific J. Math., 13, no. 3 (1963), 775–1029), rendering unnecessary the detailed use of generators and relations.