Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1-Reference-Cited by-同舟云学术

Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1

Published:1999-02-18 Issue:7 Volume:127 Page:1923-1925
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Berrizbeitia Pedro,Berry T.

Abstract

Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form A .3 n ± 1 A.3^n \pm 1 . The test for A .3 n − 1 A.3^n-1 is a minor improvement on a test derived by Williams by other means; the test for A .3 n + 1 A.3^n+1 seems to be new.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1999-127-07/S0002-9939-99-04786-3/S0002-9939-99-04786-3.pdf

Reference6 articles.

1. Effective primality tests for integers of the forms 𝑁=𝑘⋅3ⁿ+1 and 𝑁=𝑘⋅2^{𝑚}3ⁿ+1;Guthmann, Andreas;BIT,1992

2. Graduate Texts in Mathematics;Ireland, Kenneth F.,1982

3. A proof of the Lucas-Lehmer test;Rosen, Michael I.;Amer. Math. Monthly,1988

4. The primality of 𝑁=2𝐴3ⁿ-1;Williams, H. C.;Canad. Math. Bull.,1972

5. A note on the primality of 6^{2ⁿ}+1 and 10^{2ⁿ}+1;Williams, H. C.;Fibonacci Quart.,1988

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