Module MA 2 C 03 : Discrete Mathematics
نویسندگان
چکیده
41 Elementary Number Theory 92 41.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 92 41.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 92 41.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 93 41.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 96 41.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 97 41.6 The Infinitude of Primes . . . . . . . . . . . . . . . . . . . . . 98 41.7 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 41.8 Computing Powers in Modular Arithmetic . . . . . . . . . . . 100 41.9 The Chinese Remainder Theorem . . . . . . . . . . . . . . . . 102 41.10Fermat’s Little Theorem . . . . . . . . . . . . . . . . . . . . . 104
منابع مشابه
The asymptotic number of claw-free cubic graphs
Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for Hn. Here
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In this paper we study the spectrum of super–simple (v, 5, 2)– designs. We show that a super–simple (v, 5, 2)–design exists if and only if v ≡ 1 or 5 (mod 10), v 6= 5, 15, except possibly when v ∈ {75, 95, 115, 135, 195, 215, 231, 285, 365, 385, 515}.
متن کاملEmbedding Steiner triple systems into Steiner systems S(2, 4, v)
We initiate a systematic study of embeddings of Steiner triple systems into Steiner systems S(2; 4; v). We settle the existence of an embedding of the unique STS(7) and, with one possible exception, of the unique STS(9) into S(2; 4; v). We also obtain bounds for embedding sizes of Steiner triple systems of larger orders. c © 2003 Elsevier B.V. All rights reserved.
متن کاملStrong qualitative independence
The subsets A, B of the n-element X are said to be s-strongly separating if the two sets divide X into 4 sets of size at least s. The maximum number h(n, s) of pairwise s-strongly separating subsets was asymptotically determined by Frankl [8] for fixed s and large n. A new proof is given. Also, estimates for h(n, cn) are found where c is a small constant.
متن کاملPostscript: "Endomorphism spectra of graphs" [Discrete Mathematics 109 (1992) 45-57]
We answer some questions about the existence of graphs with a given endotype posed in B* ottcher and Knauer (Discrete Math. 109 (1992) 45–57). All de8nitions and needed terminology can be found there and for brevity they will not be repeated here. All results have been obtained by computer calculations. c © 2003 Elsevier B.V. All rights reserved. MSC: 05C
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