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Generalized irregular primes
Published online by Cambridge University Press: 26 February 2010
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A prime p > 2 is called irregular, if it divides the numerator of at least one of the Bernoulli numbers B2, B4, …, Bp – 3 (in the even suffix notation). The study of irregular primes has its origin in the famous theorem of Kummer which states that p divides the class number of the p-th cyclotomic field, if, and only if, p is irregular. Carlitz [1] has given the simplest proof of the fact that the number of irregular primes is infinite.
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