Number Theory pp 399-446 | Cite as

A Character Study

  • W. A. Coppel
Part of the Universitext book series (UTX)


Let a and m be integers with \(1 \leq a < m\). If a and m have a common divisor d > 1, then no term after the first of the arithmetic progression
$$a, a + m, a + 2m,\ldots$$
is a prime. Legendre (1788) conjectured, and later (1808) attempted a proof, that if a and m are relatively prime, then the arithmetic progression (*) contains infinitely many primes.


Irreducible Representation Conjugacy Class Irreducible Character Arithmetic Progression Frobenius Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • W. A. Coppel
    • 1
  1. 1.GriffithAustralia

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