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Finite projective planes and a question about primes

Author: Walter Feit
Journal: Proc. Amer. Math. Soc. 108 (1990), 561-564
MSC: Primary 51E15; Secondary 05B10, 51A35
MathSciNet review: 1002157
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Abstract: Let $ n$ be an even integer not divisible by 3. Suppose that $ p = {n^2} + n + 1$ is a prime and $ {2^{n + 1}} \equiv 1\left( {\bmod p} \right)$. The question is asked whether this can only occur if $ n$ is a power of 2. It is noted that an affirmative answer to this question implies that a finite projective plane with a flag transitive collineation group is Desarguesian.

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Keywords: Finite projective plane, flag transitive, prime
Article copyright: © Copyright 1990 American Mathematical Society

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