MathDB

A positive integer

k\geqslant 3

is called fibby if there exists a positive integer

n

and positive integers

d_1 < d_2 < \ldots < d_k

with the following properties: \\

\bullet

d_{j+2}=d_{j+1}+d_j

for every

j

satisfying

1\leqslant j \leqslant k-2

, \\

\bullet

d_1, d_2, \ldots, d_k

are divisors of

n

, \\

\bullet

any other divisor of

n

is either less than

d_1

or greater than

d_k

.
Find all fibby numbers. \\ \\ Proposed by Ivan Novak.

Problem Statement