Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Cubic reciprocity and generalised Lucas-Lehmer tests for primality of $A.3^n\pm 1$

Author(s): Pedro Berrizbeitia; T. G. Berry
Journal: Proc. Amer. Math. Soc. 127 (1999), 1923-1925.
MSC (1991): Primary 11A51, 11Y11
Posted: February 18, 1999
MathSciNet review: 1487359
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Abstract: Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form $A.3^n \pm 1$ . The test for is a minor improvement on a test derived by Williams by other means; the test for seems to be new.

References:

[G]: A. Guthmann. Effective primality tests for $N=k\cdot 3^{n+1}$ and $N=k\cdot 2^m 3^n +1$ . BIT 32 (1992) 529-534. MR 93h:11008
[IR]: K. Ireland and M. Rosen. A classical Introduction to Modern Number Theory. Springer-Verlag, Berlin, 1982. MR 83g:12001
[R]: M. Rosen. A proof of the Lucas-Lehmer test. Amer. Math. Monthly 95 (1988) 855-856. MR 89i:11011
[W1]: H. C. Williams The primality of . Can. Math. Bull. 15 (1972) 585-589. MR 47:121
[W2]: H. C. Williams. A note on the primality of $6\sp{2\sp n}+1$ and $10 \sp{2\sp n}+1$ . Fibonacci Quart. 26 (1988) 296-305. MR 89i:11013
[W3]: H.C. Williams A class of primality tests for trinomials which includes the Lucas-Lehmer test. Pacific J. Math 98 (1982) 477-494. MR 83f:10008

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