- Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi
- Vol: 23 Issue: 4
- Mulatu Numbers That Are Concatenations of Two Lucas Numbers
Mulatu Numbers That Are Concatenations of Two Lucas Numbers
Authors : Fatih Erduvan
Pages : 914-920
Doi:10.35414/akufemubid.1240679
View : 42 | Download : 57
Publication Date : 2023-08-31
Article Type : Research Article
Abstract :In this paper, we find that all Mulatu numbers, which are concatenations of two Lucas numbers are 11,17,73,118. Let 〖(M_k)〗_(k≥0) and 〖(L_k)〗_(k≥0) be the Mulatu and Lucas sequences. That is, we solve the Diophantine equation M_k=L_m L_n=10^d L_m+L_n in non-negative integers (k,m,n,d), where d denotes the number of digits of L_n. Solutions of this equation are denoted by (k,m,n,d)=(4,1,1,1),(5,1,4,1),(8,4,2,1),(9,1,6,2). In other words, we have the solutions M_4=L_1 L_1=11, M_5=L_1 L_4=17, M_8=L_4 L_2=73, M_9=L_1 L_6=118. The proof based on Baker’s theory and we used linear forms in logarithms and reduction method to solve of this Diophantine equation.Keywords : Lucas sayıları, Mulatu sayıları, Logaritmalarda lineer formlar, Diophantine denklemleri