# zbMATH — the first resource for mathematics

Primality tests using algebraic groups. (English) Zbl 1066.11055
The author using algebraic groups over $${\mathbb Q}$$ with some good properties of reduction modulo a prime, generalizes the classical primality tests of Fermat, Miller-Rabin and Pocklington. Moreover, new primality tests using recurrence sequences are presented.

##### MSC:
 11Y11 Primality 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11A51 Factorization; primality
Full Text:
##### References:
 [1] DOI: 10.1090/S0025-5718-1982-0658231-9 [2] Agrawal M., ”PRIMES is in P.” (2002) [3] Crandall R., Prime Numbers. (2001) [4] DOI: 10.1145/320211.320213 · Zbl 1064.11503 [5] DOI: 10.1090/S0025-5718-00-01197-2 · Zbl 1011.11079 [6] Gurak S., Théorie des nombres pp 330– (1989) [7] Suwa N., ”Some Remarks on Lucas Pseudoprimes.” (2004) · Zbl 1275.11151 [8] Voskresenskii V. E., Algebraic Groups and Their Birational Invariants (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.