I. Borosh

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Wythoff s game is a variation of Nim, a two-pile game in which each player removes counters in turn until the winner takes the last counter. The safe-pairs generated in the solution of Wythoff's game have many properties interesting in themselves, and are related to the canonical Zeckendorf representation of an integer using Fibonacci numbers. In Nim, the(More)
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 =(More)
WSPC/Book Trim Size for 9in x 6in justchapter7 Preface The main justification for this book is that there have been significant advances in continued fractions over the past decade, but these remain for the most part scattered across the literature, and under the heading of topics from algebraic number theory to theoretical plasma physics. We now have a(More)
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