On the Diophantine equation ((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m^{2}+1)^{x}+(cm^{2}-1)^{y}=(am)^z

Elif KIZILDERE; Takafumi MIYAZAKI; Gökhan SOYDAN

Makale detayları

On the Diophantine equation ((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m^{2}+1)^{x}+(cm^{2}-1)^{y}=(am)^z

Yazarlar:

Elif KIZILDERE | Takafumi MIYAZAKI | Gökhan SOYDAN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2690-2698

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745791

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Suppose that ccc, mmm, and aaa are positive integers with a≡11,13(mod24)a≡11,13(mod24)a \equiv 11,\,13 \pmod{24}.   In this work, we prove that when 2c+1=a22c+1=a22c+1=a^{2}, the Diophantine equation in the title has only solution (x,y,z)=(1,1,2)(x,y,z)=(1,1,2)(x, y, z)=(1,1,2) where m≡±1(moda)m≡±1(moda)m \equiv \pm 1 \pmod{a} and m>a2m>a2m>a^2 in positive integers. The main tools of the proofs are elementary methods and Baker's theory.

Makale detayları

On the Diophantine equation ((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m2+1)x+(cm2−1)y=(am)z((c+1)m^{2}+1)^{x}+(cm^{2}-1)^{y}=(am)^z

Yazarlar: Elif KIZILDERE | Takafumi MIYAZAKI | Gökhan SOYDAN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2690-2698

Belge Tipi: Makale

Yayın Tarihi: 9/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745791

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Elif KIZILDERE | Takafumi MIYAZAKI | Gökhan SOYDAN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2690-2698

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745791

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098