Fibonacci and Lucas numbers as products of two repdigits

Authors: FATİH ERDUVAN, REFİK KESKİN

Abstract: In this study, it is shown that the largest Fibonacci number that is the product of two repdigits is $F_{10}=55=5\cdot 11=55\cdot 1$ and the largest Lucas number that is the product of two repdigits is $L_{6}=18=2\cdot 9=3\cdot 6.$

Keywords: Fibonacci number, Lucas number, repdigit, Diophantine equations, linear forms in logarithms

Full Text: PDF