A Test for Divisibility
نویسندگان
چکیده
منابع مشابه
Divisibility Test for Lacunary Polynomials
Given two lacunary (i.e. sparsely-represented) polynomials with integer coefficients, we consider the decision problem of determining whether one polynomial divides the other. In the manner of Plaisted [6], we call this problem 2SparsePolyDivis. More than twenty years ago, Plaisted identified as an open problem the question of whether 2SparsePolyDivis is in P [7]. Some progress has been made si...
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Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملPerfect divisibility and 2-divisibility
A graph G is said to be 2-divisible if for all (nonempty) induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that ω(A) < ω(H) and ω(B) < ω(H). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that H[A] is perfect and ω(B) < ω(H). We prove that if a graph is (P5, C5)-free, then it is 2-divisibl...
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• Let R be a ring. Let u ∈ N and v ∈ N, and let ai,j be an element of R for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . Then, we denote by (ai,j) 1≤i≤u the u× v matrix A ∈ Ru×v whose entry in row i and column j is ai,j for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . • Let R be a commutative ring with unity. Let P ∈ R [X] be a polynomial. Let j ∈ N. Then, we denote by coeffj P the coef...
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Article history: Received 9 October 2015 Received in revised form 24 November 2015 Accepted 26 November 2015 Available online 8 January 2016 Communicated by Steven J. Miller MSC: 11B39
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ژورنال
عنوان ژورنال: Nature
سال: 1897
ISSN: 0028-0836,1476-4687
DOI: 10.1038/057008b0