On the diophantine equation \(1+x+y=z\)
type: Item
instance of: scholarly article
title: On the diophantine equation \(1+x+y=z\)
zbMATH Open document ID: 0760.11013
author: Leo J. Alex
author: Lorraine L. Foster
published in: Rocky Mountain Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The authors use some elementary technics developed by them and J. L. Brenner, to solve the equation \(1+x+y=z\) in positive integers \(x,y,z\) divisible only by 2,3,5. The method involves the careful consideration of the equation modulo a series of primes, prime powers and other moduli. First, the simpler case is considered, when \(xyz\) is divisible by at most two of 2,3,5 only. In the general case elementary properties of the equation are established, together with bounds for certain exponents. The solutions with ``small'' exponents are found with computer assistence.
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 61916
zbMATH Keywords: \(S\)-unit equation
zbMATH Keywords: exponential diophantine equation
reviewed by: István Gaál
MaRDI profile type: Publication
Wikidata QID: Q60174250
full work available at URL: https://doi.org/10.1216/rmjm/1181072793
OpenAlex ID: W2002605556
cites work: Diophantine equations related to finite groups
cites work: Simple groups and a Diophantine equation
cites work: On diophantine equations of the form 1+2**alpha=(p**i)(q**j)+(2**k)(p**m)(q**n)
cites work: On the diophantine equation \(1+p^ a=2^ b+2^ c\,p^ d\)
cites work: Exponential diophantine equations
cites work: Q4106278
DOI: 10.1216/RMJM/1181072793
description: scientific article; zbMATH DE number 61916