Results 1 to 10 of about 12,798,996 (387)
On the number of false witnesses for a composite number [PDF]
Mathematics of Computation, 1986 Ifais not a multiple ofnandan−1≢1modn{a^{n - 1}}\;\nequiv \;1\bmod \,n, thennmust be composite andais called a "witness" forn. LetF(n)F(n)denote the number of "false witnesses" forn, that is, the number ofamodna\bmod nwithan−1≡1modn{a^{n - 1}} \equiv 1\bmod n. Considered here is the normal and average size ofF(n)F(n)forncomposite.
Paul Erdős, Carl Pomerance
semanticscholar +4 more sources
Bad witnesses for a composite number [PDF]
Acta Arithmetica, 2023 We describe the average sizes of the set of bad witnesses for a pseudo-primality test which is the product of a multiple-rounds Miller-Rabin test by the Galois test.
Legnongo, Johnathan Djella +2 more
openaire +3 more sources
The crossing number of composite knots [PDF]
Journal of Topology, 2008 It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K'
Lackenby, Marc
core +3 more sources
Relation between Prime and Composite Number
Bibechana, 2018 This article was not peer-reviewed. No abstract available.
Raju Ram Thapa
doaj +4 more sources
The Twentieth Fermat Number is Composite [PDF]
Mathematics of Computation, 1988 The twentieth Fermat number, F 20 = 2 2 20 + 1 {F_{20}
Jeff Young, Duncan A. Buell
openalex +3 more sources
On the number of terms of a composite polynomial [PDF]
Acta Arithmetica, 2007 n ...
Umberto Zannier
openalex +4 more sources
Composite Rational Functions and Arithmetic Progressions [PDF]
arXiv, 2017 In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed number of zeros and poles.
Tengely, Szabolcs
arxiv +5 more sources
On compositions of natural numbers [PDF]
arXiv, 2020 In this expository note, we introduce the reader to compositions of a natural number, e.g., $2+1+2+1+7+1$ is a composition of 14, and $1+2$ and $2+1$ are two different compositions of 3. We discuss some simple restricted forms of compositions, e.g., $23+17+33$ is a composition of 73 into three odd parts.
arxiv +3 more sources
On Number of Compositions of Natural Numbers [PDF]
arXiv, 2010 We first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a relationship between the number of compositions of a natural number in which a certain number of parts are p-1, and other parts are not less than p with compositions in which all
arxiv +3 more sources
Maximum occupation number for composite boson states [PDF]
, 2002 One of the major differences between fermions and bosons is that fermionic states have a maximum occupation number of one, whereas the occupation number for bosonic states is in principle unlimited.
D. VAN NECK +6 more
core +2 more sources