We introduce a two person game played with a pair of nonnegative integers; a move consists of subtracting from the larger integer, a positive integer no greater than the smaller integer. The player who reduces one of the integers to zero wins. The game is curious in several respects: in particular, its Sprague-Grundy values have an interesting connection with prime numbers.

Since any personal computer has a limited range of integer values, therefore, it will result in an integer overflow when a program tries to compute a value larger than machine’s maximum value. We will discuss a workable algorithm that will be able to deal with any large numbers without getting an integer overflow.

For 1 i k, let Ri denote pi(y)Fi + Gi , where pi(y) is a polynomial in y with integer coefficients, and Fi,Gi are linear polynomials in x1, . . . , xn with integer coefficients. Let P(z1, . . . , zk) be a Presburger relation over the nonnegative integers. We show that the following problem is decidable: Given: R1, . . . , Rk and a Presburger relation P. Question:Are there nonnegative integer va...

This paper presents techniques for handling symmetries in integer linear programs where variables can take integer values, extending previous work dealing exclusively with binary variables. Orthogonal array construction and coloring problems are used as illustrations.

In this paper we give new, improved explicit upper bounds for the absolute values of the integer solutions and for the heights of S-integer solutions of elliptic equations over Q.

In this paper, we propose a new model for designing integrated forward/reverse logistics based on pricing policy in direct and indirect sales channel. The proposed model includes producers, disposal center, distributers and final customers. We assumed that the location of final customers is fixed. First, a deterministic mixed integer linear programming model is developed for integrated logistic...

Given a positive integer A 6= 2. In this paper, we show that there do not exist two positive integer pairs {a, b} 6= {c, d} such that the values of ac+ 1, ad+ 1 and bc+ 1, bd+ 1 are the terms of the sequence {Gn}n≥0 which satisfies the recurrence relation Gn = AGn−1 − Gn−2 with the initial values G0 = 0, G1 = 1.