×

The Euler totient function on quadratic fields. (English) Zbl 1499.11015

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11R11 Quadratic extensions
13M10 Polynomials and finite commutative rings
Full Text: DOI

References:

[1] L. E. Dickson, A generalization of Fermat’s theorem, Ann. Math. (2) 1(1/4) (1899-1900), 31-36. · JFM 30.0185.01
[2] C. Y. Chao, Generalizations of theorems of Wilson, Fermat and Euler, J. Number Theory 15(1) (1982), 95-114. · Zbl 0489.10002
[3] James T. Cross, The Euler -function in the Gaussian integers, Amer. Math. Monthly 90(8) (1983), 518-528. · Zbl 0525.12001
[4] J. Díaz Vargas and H. Tapia Recillas, La functión  de Euler en los Enteros de Eisenstein-Jacobi, Reportes de Investigación, Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, 1989.
[5] F. S. Gillespie, A generalization of Fermat’s little theorem, Fibonacci Quart. 27(2) (1989), 109-115. · Zbl 0672.10010
[6] M. Lassák and S. Porubsky, Fermat-Euler theorem in algebraic number fields, J. Number Theory 60(2) (1996), 254-290. · Zbl 0877.11069
[7] A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997. · Zbl 0868.94001
[8] E. H. Moore, A two-fold generalization of Fermat’s theorem, Bull. Amer. Math. Soc. 2(7) (1896), 189-199. · JFM 27.0139.05
[9] I. Niven and L. J. Warren, A generalization of Fermat’s theorem, Proc. Amer. Math. Soc. 8(2) (1957), 306-313. · Zbl 0077.26106
[10] I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, 5th ed., John Wiley & Sons Inc., 1991. · Zbl 0742.11001
[11] R. T. Harger and R. M. Smith, A generalization of Fermat’s little theorem, Internat. J. Math. Ed. Sci. Tech. 31(3) (2000), 476-477. Doi: 10.1080/00207390050032351. · Zbl 1033.11500 · doi:10.1080/00207390050032351
[12] B. Schneier, Applied Cryptography, John Wiley & Sons Inc. 2nd ed., 1966.
[13] W. Sierpinski, Elementary Theory of Numbers, Warsaw, 1964. · Zbl 0638.10001
[14] D. R. Stinson, Cryptography Theory and Practice, CRC Press, 1995. · Zbl 0855.94001
[15] A. V. Zarelua, On matrix analogues of Fermat’s little theorem, Math. Notes 79(5-6) (2006), 783-796. · Zbl 1136.11022
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.