Primes in Certain Arithmetic Progressions
Ram Murty and Nithum Thain
Source: Funct. Approx. Comment. Math. Volume 35, Number 1
(2006), 249-259.
Abstract
We discuss to what extent Euclid's elementary proof of the infinitude of primes can be modified so as to show infinitude of primes in arithmetic progressions (Dirichlet's theorem). Murty had shown earlier that such proofs can exist if and only if the residue class (mod $k$) has order 1 or 2. After reviewing this work, we consider generalizations of this question to algebraic number fields.
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Permanent link to this document: http://projecteuclid.org/euclid.facm/1229442627
Mathematical Reviews number (MathSciNet): MR2271617
Zentralblatt MATH identifier: 05784932
Digital Object Identifier: doi:10.7169/facm/1229442627
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