Mersenne numbers as a difference of two Lucas numbers

Commentationes mathematicae Universitatis Carolinae

article

Murat Alan

关键词: Lucas number;    Mersenne number;    Diophantine equation;    linear forms in logarithm;   

DOI  :  10.14712/1213-7243.2022.027

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Let (L_n)_{n\geq 0} be the Lucas sequence. We show that the Diophantine equation L_n-L_m=M_k has only the nonnegative integer solutions (n,m,k)= (2,0,1), (3, 1, 2), (3, 2, 1), (4, 3, 2), (5, 3, 3), (6, 2, 4), (6, 5, 3) where M_k=2^k-1 is the kth Mersenne number and m.

【 授权许可】

CC BY