Nonnegative integer solutions of the equation Fn−Fm=5aFn−Fm=5aF_{n}-F_{m}=5^{a}

Fatih ERDUVAN; Refik KESKİN

Makale detayları

Nonnegative integer solutions of the equation Fn−Fm=5aFn−Fm=5aF_{n}-F_{m}=5^{a}

Yazarlar:

Fatih ERDUVAN | Refik KESKİN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1115-1123

Belge Tipi:

Makale

Yayın Tarihi:

5/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745585

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this study, we solve the Diophantine equation in the title in nonnegative  integers m,n,m,n,m,n, and aaa. The solutions are given by   F1−F0=F2−F0=F3−F2=F3−F1=F4−F3=50F1−F0=F2−F0=F3−F2=F3−F1=F4−F3=50F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}  and  F5−F0=F6−F4=F7−F6=5.F5−F0=F6−F4=F7−F6=5.F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.  Then we give a conjecture that says that if a≥2a≥2a\geq 2 and p>7p>7p>7 is prime,  then the equation Fn−Fm=paFn−Fm=paF_{n}-F_{m}=p^{a} has no solutions in nonnegative  integers m,n.m,n.m,n.

Makale detayları

Nonnegative integer solutions of the equation Fn−Fm=5aFn−Fm=5aF_{n}-F_{m}=5^{a}

Yazarlar: Fatih ERDUVAN | Refik KESKİN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1115-1123

Belge Tipi: Makale

Yayın Tarihi: 5/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745585

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Fatih ERDUVAN | Refik KESKİN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1115-1123

Belge Tipi:

Makale

Yayın Tarihi:

5/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745585

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098