Q: Let be an integer not divisble by 3. Suppose that is a prime and . Is a power of ?
A solution to this problem would imply that every finite flag-transitive projective plane is Desarguesian. Walter Feit obeserved this in his 1990 paper in the Proceedings of the American Mathematical Society, and he confirmed by computer that it is true for . Since then, there has been some review and survey of this problem by various authors, and I’m surprised to see that none have sat at the computer and tried to extend Feit’s computation.
So I gave it a crack myself:
The answer is “Yes” for .
This can definitely be extended by far better programmers than me … any advance on this bound?