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联立Pell方程组x~2-ay~2=1和y~2-bz~2=1的解数 总被引:1,自引:0,他引:1
设a,b是正整数.我们研究了联立Pell方程组x~2-ay~2=1,y~2-bz~2=1的正整数解(x,y,z)的个数.本文利用Bennett关于联立Padé逼近的一个结果,证明了该方程组至多只有两组正整数解(x,y,z),从而改进了Bennett(1998),袁平之(2004)等人的结论. 相似文献
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设a,b是不同的正整数,本文证明了当max(a,b)>10126时,Pell方程组x2-ay2=1和z2-by2=1至多有2组正整数解(x,y,z). 相似文献
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本文利用矩阵对的广义奇异值分解研究矩阵方程AXB=C有D对称解的充分必要必要条件,并给出了通解的表达式。 相似文献
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矩阵方程AXAT=C的对称斜反对称解 总被引:1,自引:0,他引:1
设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤. 相似文献
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We consider the equation of the title in a finite field of q elements. Assuming certain relations between n and q, we obtain explicit formulas for the number of solutions to this equation. 相似文献
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We characterize – by describing in local coordinates their sections – the transversal bundles which on the complex hypersurface with type number 1 induce locally symmetric connections. 相似文献
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矩阵方程AXAT=C的对称斜反对称解 总被引:1,自引:0,他引:1
设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤. 相似文献
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广义Ramanujan-Nagell方程x~2+D~m=p~n的解数 总被引:2,自引:0,他引:2
设a是正整数,D=3a2+1,P=4a2+1,其中p是素数.本文证明了:如果a不是4的倍数,则除了当(D,p)=(4,5)时方程x2+Dm=pn恰有3组正整数解(x,m,n)=(1,1,1),(3,2,2),(11,1,3)以外,该方程恰有2组正整数解(x,m,n)=(a,1,1)和(8a3+3a,1,3). 相似文献
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Norio Yamazaki 《Journal of Algebraic Combinatorics》1998,8(1):73-105
In this paper, we have a classification of primitive symmetric association schemes with k
1 = 3. 相似文献
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Let p, q and r be three integers 2. During the last ten years many new ideas have emerged for the study of the Diophantine equation x + y = z. This study is divided into three parts according whether (p, q, r) =
is negative, zero or positive. For instance, if we have (p, q, r) < 0, this study is closely connected to the theory of modular representations of dimension 2 in finite characteristic. The approach of associating to this equation Galois representations given by the division points of elliptic curves is very efficient. The aim of this paper is to present this circle of ideas and the known results concerning this equation. 相似文献
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We determine the group of diffeomorphisms of a bounded symmetric domain, which preserve simultaneously the hyperbolic and
the at symplectic form.
*Research partially supported by GNSAGA (INdAM) and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex
Manifolds” (PRIN05).
**Research partially supported by GNSAGA (INdAM) and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex
Manifolds” (PRIN05).
***Part of this work was done in July 2007 during a visit of G. Roos at Politecnico di Torino; visit supported by GNSAGA (INdAM)
and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex Manifolds: (PRIN05). 相似文献
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Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group, i.e., that conjugacy classes of S n do not unite under the natural representation. We prove this fact, and give its application to the enumeration of fixed points under a natural action of S n × S n . We also consider the permutation representations of S n which arise from the action of S n on ordered tuples and on unordered subsets, and classify which of them unite conjugacy classes and which do not. 相似文献
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设D是不能被3整除的正整数.本文证明了:当D>1012时,如果Pell方程U2-DV2=-1有解(U,V),则方程x2-D=3n至多有2组正整数解(x,n). 相似文献
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In this paper we give first a new combinatorial interpretation of the coefficients of chromatic polynomials of graphs in terms of subsets of permutations. Motivated by this new interpretation, we introduce next a combinatorially defined polynomial associated to a directed graph, and prove that it is related to chromatic polynomials. These polynomials are a specialization of cover polynomials of digraphs.I am grateful to the Swiss National Science Foundation for its partial financial supportFinal version received: June 25, 2003 相似文献