On integer solutions to x² - dy² = 1, z² - 2dy² =1

A Simple Criterion for Solvability of Both X2-DY2= c and x2-Dy2=-c

This article provides a simple criterion for the simultaneous solvability of the Diophantine equations X2 −DY 2 = c and x2 −Dy2 = −c when c ∈ Z, and D ∈ N is not a perfect square.

" - Optimal Solutions to Nonlinear 0 - 1 Integer Programs Using theSubgradient

In the context of the 1993-1994 DIMACS special year on Parallel Computing, a two-day work-shop entitled \Parallel Processing of Discrete Optimization Problems" was held on April 28{29.The workshop featured about twenty invited speakers from Europe and North America. Thisreport containts the abstracts of the talks. A DIMACS volume with complete refereed papersfrom the worksho...

Integer Valued AR(1) with Geometric Innovations

The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...

On the largest prime factor of x2-1

In this paper, we find all integers x such that x − 1 has only prime factors smaller than 100. This gives some interesting numerical corollaries. For example, for any positive integer n we can find the largest positive integer x such that all prime factors of each of x, x + 1, . . . , x+ n are less than 100.

ON THE DIOPHANTINE EQUATION x2+p2k+1 = 4yn