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Number Theory pp 399–446Cite as

A Character Study

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Abstract

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.

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  1. 3 Jansz Crescent, 2603, Griffith, Australia

    W. A. Coppel

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Coppel, W.A. (2009). A Character Study. In: Number Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89486-7_10

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