ON A CONJECTURE REGARDING BALANCING WITH POWERS OF FIBONACCI NUMBERS

摘要

Here, we show that (k, !, n, r) = (8, 2, 4, 3) is the only solution in positive integers of the Diophantine equation Fk 1 + Fk 2 + · · · + Fk n?1 = F! n+1 + · · · + F! n+r, where Fm is the mth Fibonacci number.