Diophantine representation of Mersenne and Fermat primes
نویسندگان
چکیده
منابع مشابه
Mersenne and Fermat Numbers
The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
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The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
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On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...
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Article history: Received 18 June 2014 Received in revised form 11 June 2015 Accepted 12 June 2015 Available online 22 June 2015 Communicated by Neal Koblitz MSC: primary 11A41, 11A07 secondary 15B99, 05C90
متن کاملFermat Numbers and Elite Primes
Fn+1 = (Fn − 1) + 1, n ≥ 0 and are pairwise coprime. It is conjectured that Fn are always square-free and that, beyond F4, they are never prime. The latter would imply that there are exactly 31 regular polygons with an odd number Gm of sides that can be constructed by straightedge and compass [2]. The values G1, G2, . . ., G31 encompass all divisors of 232−1 except unity [3]. Let G0 = 1. If we ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1979
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-35-3-209-221