On the number of solutions of certain linear diophantine equations
نویسندگان
چکیده
منابع مشابه
on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولThe Number of Solutions of Diophantine Equations
0. Introduction. In two recent papers 4], 30], Erdd os, Stewart and the author showed that certain diophantine equations have many solutions. In this way they indicated how far certain results are capable for improvements at most. First we mention some relevant results from the literature on upper bounds for the numbers of solutions of diophantine equations and then we sketch how our method lea...
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Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...
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Let Ax = B be a system of m x n linear equations with integer coefficients. Assume the rows of A are linearly independent and denote by X (respectively Y) the maximum of the absolute values of the m x m minors of the matrix A (the augmented matrix (A, B)). If the system has a solution in nonnegative integers, it is proved that the system has a solution X = (xi) in nonnegative integers with xi <...
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We present structural results on solutions to the Diophantine system Ay = b, y ∈ Z ≥0 with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel’s Lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization.
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1990
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381517487