Mathematica 9 is now available

Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

The Equation (x+1)...(x+k)=(y+1)...(y+mk) with m=3, 4
Authors

N. Saradha
T. Shorey
Journal / Anthology

Indagationes Mathematicae
Year: 1991
Volume: 2
Issue: 4
Page range: 489-510
Description

We consider the equation (x+1)...(x+k) = (y+1)...(y+mk). If m = 1, the equation implies that x = y. If m = 2, the authors showed that x = 7, y = 0, k = 3 is the only solution in integers x >= 0, y >= 0, k >= 2. In this paper, we prove that (x+1)...(x+k) = (y+1)...(y+3k) and (x+1)...(x+k) = (y+1)...(y+4k) have no solution in integers x >= 0, y >= 0, and k >= 2.
Subject

*Mathematics > Algebra > Polynomials