Mersenne primes in real quadratic fields

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dc.contributor.authorPalimar, S.
dc.contributor.authorShankar, B.R.
dc.date.accessioned2026-02-05T09:35:18Z
dc.date.issued2012
dc.description.abstractThe concept of Mersenne primes is studied in real quadratic fields with class number one. Computational results are given. The field ?(?2) is studied in detail with a focus on representing Mersenne primes in the form x2 + 7y2. It is also proved that x is divisible by 8 and y ? ±3 (mod 8), generalizing a result of F. Lemmermeyer, first proved by H. W. Lenstra and P. Stevenhagen using Artin's reciprocity law.
dc.identifier.citationJournal of Integer Sequences, 2012, 15, 5, pp. -
dc.identifier.issn15307638
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/26999
dc.subjectArtin's reciprocity law
dc.subjectMersenne primes
dc.titleMersenne primes in real quadratic fields

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