Interesting Esoterica

Prime numbers in certain arithmetic progressions

by Ram Murty and Nithum Thain
  • Published in 2001
  • Added on
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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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Other information

key
item61
type
misc
date_added
2016-05-07
date_published
2001-05-24

BibTeX entry

@misc{item61,
	key = {item61},
	type = {misc},
	title = {Prime numbers in certain arithmetic progressions},
	author = {Ram Murty and Nithum Thain},
	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.},
	comment = {},
	date_added = {2016-05-07},
	date_published = {2001-05-24},
	urls = {http://projecteuclid.org/download/pdf{\_}1/euclid.facm/1229442627},
	collections = {Fun maths facts,Integerology},
	url = {http://projecteuclid.org/download/pdf{\_}1/euclid.facm/1229442627},
	urldate = {2016-05-07},
	year = 2001
}