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Schwarz, Štefan

The role of semigroups in the elementary theory of numbers. (English) Zbl 0474.10002

Math. Slovaca 31, 369-395 (1981).
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Cited in 1 Review
Cited in 12 Documents

MSC:

11A07 Congruences; primitive roots; residue systems
20M10 General structure theory for semigroups
20M25 Semigroup rings, multiplicative semigroups of rings

Keywords:

Euler-Fermat theorem; Wilson theorem; multiplicative semigroup; idempotents

Citations:

Zbl 0111.034
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\textit{Š. Schwarz}, Math. Slovaca 31, 369--395 (1981; Zbl 0474.10002)
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References:

[1] CORDES C. M.: Permutations mod m in the form xn. Amer. Math. Monthly 83, 1976, 32-33. · Zbl 0328.10003
[2] HEWITT E., ZUCKERMAN H. S.: The multiplicative semigroup of integers (mod m). Pacific J. Math. 10, 1960, 1291-1308. · Zbl 0115.02402
[3] HEWITT E.: Certain congruences that hold identically. Amer. Math. Monthly 83, 1976, 270-271. · Zbl 0319.10003
[4] KOWOL G., MITSCH H.: Polynomial functions over commutative semigroups. Semigroup Forum 12, 1976, 109-118. · Zbl 0338.20089
[5] LIVINGSTON A. E., LIVINGSTON M. L.: The congruence \(a^{r+s} = a^s (mod m)\). Amer. Math. Monthy 85, 1978, 97-100. · Zbl 0375.10002
[6] MORGADO J.: A property of the Euler \(\varpsi\)-function concerning the integers which are regular (mod m). Portugal. Math. 33, 1974, 185-191. · Zbl 0302.10003
[7] OSBORN R.: A ”good” generalization of the Euler-Fermat theorem. Math. Mag. 47, 1974, 28-31. · Zbl 0276.10003
[8] PARÍZEK B., SCHWARZ Š.: O multiplikatívnej pologrupe zvyškových tried (mod m). Mat.-Fyz. Časop. 8, 1958, 136-150.
[9] PARÍZEK B.: O rozklade pologrupy zvyškov (mod m) na direktný súčin. Mat.-Fyz. Časop. 10, 1960, 18-29.
[10] SINGMASTER D.: A maximal generalization of Ferma\?s theorem. Math. Mag. 39, 1966, 103-107. · Zbl 0151.03303
[11] SMALL, CH.: Powers mod m. Math. Mag. 50, 1977, 84-86. · Zbl 0351.10003
[12] VANDIVER H. S., WEAVER H. W.: Introduction to arithmetic factorization and congruences from the standpoint of abstract algebra. H. E. Slaught Memorial Papers, no. 7, 1958, Math. Assoc. of America. · Zbl 0084.27002
[13] ZANE B.: Uniform distribution (mod m) of monomials. Amer. Math. Monthly 71, 1964, 162-164. · Zbl 0122.06001
[14] BUCHŠTAB A. A.: Teorija čisel. Gos. uč.-ped. izd., Moskva, 1960.
[15] DICKSON L. E., BODEWIG E.: Introduction to the Theory of Numbers. (German edition.) Teubner, Leipzig, 1931.
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.