Repdigits Base b as Difference of Two Fibonacci Numbers

Zafer S¸iar,Fatih Erduvanand Refik Keskin,∗

1Bing¨ol University,Department of Mathematics,Bing¨ol 12000,Turkey.

2Sakarya University,Department of Mathematics,Sakarya TR-54187,Turkey.

Abstract.In this paper,we find all repdigits expressible as difference of two Fibonacci numbers in base b for 2≤b≤10.The largest repdigits in base b,which can be written as difference of two Fibonacci numbers are

Key words:Fibonacci numbers,repdigit,Diophantine equations,linear forms in logarithms.

1 Introduction

2 Auxiliary results

3 Main theorem

Acknowledgments

We thank the referee for his/her suggestions which improved the quality of this paper.