On the Exponential Diophantine Equation (m(2) + m+1)(x) + m(y) = (m+1)(z)

ALAN M.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.17, no.6, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.1007/s00009-020-01613-4
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Yıldız Technical University Affiliated: Yes

Abstract

Let m >= 1 be a positive integer. We show that the exponential Diophantine equation (m(2) + m + 1)(x) + m(y) = (m + 1)(z) has no positive integer solutions other than (x, y, z) = (1, 1, 2) when m is not an element of {1, 2, 3}.