Keywords:-

Keywords: Fermat numbers, Legendre’s symbol, polynomials factorization, law of quadratic reciprocity

Article Content:-

Abstract

Let p be a prime integer and let k ∈N. We purpose a factorization of X2k +1 (mod p) allowing ti give a primality criterion for Fermat numbers.

Mathematics Subject Classification 2010 11A07 11 A 51

References:-

References

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J.C. Morehead and A.E. Western, Note on Fermat’s numbers, Bull. Amer. Math. Soc. 16 (1909), n˚1, 1-6.

G.A. Paxson, The compositeness of the thirteenth Fermat number, Math. Comp. 15 (1961), 420.

R.M. Robinson, Mersenne and Fermat numbers, Proc. Amer. Math. Soc. 5 (1954), 842-846.

S. Roman, Coding and Information theory; Irvine, Springer-Verlag, New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest, 1991.

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FALL, O., & Bachir DEME, C. (2022). Polynomial Factorization and Primality Criterion for Fermat Numbers. International Journal Of Mathematics And Computer Research, 10(2), 2579-2580. https://doi.org/10.47191/ijmcr/v10i2.05