ON THE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATION x(2)+2(a) . p(b) = y(4)

Zhu H., Le M., Soydan G.

MATHEMATICAL REPORTS, vol.17, no.3, pp.255-263, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 3
  • Publication Date: 2015
  • Journal Name: MATHEMATICAL REPORTS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.255-263
  • Keywords: exponential Diophantine equation, Lebesgue-Nagell equation, classification of solutions
  • Bursa Uludag University Affiliated: Yes

Abstract

Let p be a fixed odd prime. In this paper, we study the integer solutions (x, y, a, b) of the equation x(2) + 2(a).p(b) = y(4), gcd(x, y) = 1, x > 0, y > 0, a >= 0, b >= 0, and we derive upper bounds for the number of such solutions.