A large number of papers is devoted to the study of simultaneous Pell equations; they could be classified into three categories: The first one includes papers, in which results are proved of the type “there are no solutions”, or “there are at most k solutions”, where k is a number ...
We consider a diagonal equation, which can be reduced to the form[x_1^2+cdots+x_{n-2}^2+x_{n-1}^k+x_n^k=0,]over a finite field of characteristic p > 2. In 1997, Sun obtained the explicit formula for the number of solutions to an equation of this type when n is even. ...
57 PINK ISTVÁN_ NUMBER OF SOLUTIONS TO A SPECIAL TYPE OF UNIT EQUATIONS IN TWO UNKN 1:19:49 RUZSA IMRE_ HÉZAGOS BEURLING 51:34 ZÁBRÁDI GERGELY_ THE SUP-NORM PROBLEM FOR AUTOMORPHIC CUSP FORMS OF PGL(N,Z[I]), 1:40:34 EMMANUEL KOWALSKI_ SIDON SETS IN ALGEBRAIC GEOMETRY 1:...
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View PDFReferences 1. S. Agmon, A. Douglis, L. Nirenberg Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I Comm. Pure Appl. Math., XII (1959), pp. 623-727 CrossrefView in ScopusGoogle Scholar 2. H. Amann On the ...
1. Introduction Let Fq denote the finite field of order q = 2'. Let N ( s , n , r ) denote the number of s x n matrices X over Fq that satisfy the equation (1.1) X X T = 0, where X T denotes the transpose of X . PERKINSIhas proved first that [ ] (1.3) N
The most familiar irrational numbers are algebraic numbers, which are the roots of algebraic equations with integer coefficients. For example, the solution to the equation x2 − 2 = 0 is an algebraic irrational number, indicated by Square root of√2. Some irrational numbers, such as π and...
and powers in which all the constants are integers and the only solutions of interest are integers. For example, 3x+ 7y= 1 orx2−y2=z3, wherex,y, andzare integers. Named in honour of the 3rd-century Greek mathematicianDiophantus of Alexandria, these equations were first systematically so...
APPLICATION OF SOME INTEGRAL EQUATIONS TO PROBLEMS OF NUMBER THEORY CONTENTS Basic notation Introduction Chapter I. Auxiliary lemmas §1. The functions , , , and their properties §2. Estimates for the solutions of some app... BV Levin,AS Fainleib - 《Russian Mathematical Surveys》 被引量: 83...
support solutions of (systems of) linear diophantine and linear congruence equations (with one or many variables) [DONE] add Rank Factorisation [DONE] fix ginv (Moore-Penrose Inverse) computation [DONE] implement (faster) numeric EVD/SVD computation (TODO) support general and least-squares solutio...