ON A LINEAR DIOPHANTINE PROBLEM INVOLVING THE FIBONACCI AND LUCAS SEQUENCES

摘要

For a positive and relatively prime set A, let (A) denote the set of integers that are formed by taking nonnegative integer linear combinations of integers in A. Then there are finitely many positive integers that do not belong to (A). For A, let g(A) and n(A) denote the largest integer and the number of integers that do not belong to (A), respectively. We determine both g(A) and n(A) for two sets that arise naturally from the Fibonacci sequence and the Lucas sequence.