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

Zhu, Huilin; Le, Maohua; Soydan, GÖKHAN

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

MATHEMATICAL REPORTS, cilt.17, sa.3, ss.255-263, 2015 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 17 Sayı: 3
Basım Tarihi: 2015
Dergi Adı: MATHEMATICAL REPORTS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.255-263
Anahtar Kelimeler: exponential Diophantine equation, Lebesgue-Nagell equation, classification of solutions
Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.