ON DIOPHANTINE EQUATIONS INVOLVING SUMS OF FIBONACCI NUMBERS AND POWERS OF 2

摘要

In this paper, we completely solve the Diophantine equations Fn1 + Fn2 = 2a1 + 2a2 + 2a3 and Fm1 + Fm2 + Fm3 = 2t1 + 2t2 , where Fk denotes the k-th Fibonacci number. In particular, we prove that max{n1, n2, a1, a2, a3} ? 18 and max{m1, m2, m3,t1,t2} ? 16.