A note on the ternary purely exponential diophantine equation A(x) + B-y = C-z with A plus B = C-2

Kizildere E., le M., SOYDAN G.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.57, no.2, pp.200-205, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1556/012.2020.57.2.1457
  • Journal Name: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.200-205
  • Keywords: Ternary purely exponential Diophantine equation, BHV theorem on the existence of primitive divisors of Lehmer numbers
  • Bursa Uludag University Affiliated: Yes

Abstract

Let l,m,r be fixed positive integers such that 2 vertical bar l, 3 lm, l > r and 3 vertical bar r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm(2) - 1,(l-r)lm(2) + 1} >30, then the equation (rlm(2) - 1)(x) + ((l - r)lm(2) + 1)(y) = (lm)(z) only the positive integer solution (x,y,z) = (1,1,2).