Generalization of Fermat’s Little Theorem

MJ Sanada Khumanthem; Kh. Manglem Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V65I7P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P509

Generalization of Fermat’s Little Theorem

MJ Sanada Khumanthem , Kh. Manglem Singh

Citation :

MJ Sanada Khumanthem , Kh. Manglem Singh, "Generalization of Fermat’s Little Theorem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 56-59, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P509

Abstract

There are different methods to decide whether an integer is prime. Fermat’s little theorem is the generalization of 2n-1 ≡1 mod n,while AKS test is the generalization of Fermat’s little theorem. Fermat’s little theorem is probabilistic method, while AKS test is deterministic one. The first method is faster, but not guaranteed, and the second one is guaranteed, but slow.

Keywords

Prime, Fermat’s little theorem, AKS test, Pascal' triangle, Binomial expansion

References

[1] C.P. Bauer, Secret history, the story of cryptology, CRC Press, 2013.
[2] M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. of Math., 160(2), 781-793, 2004.
[3] S. Aaronson, The prime facts: from Euclid to AKS, 2003, https://www.scottaaronson. com/writings/prime.pdf (accessed on 07/07/2019).