Y by
Let
be an integer. The sequence
is defined via
,
and
for any positive integer
. Prove that there are finitely many pairs
of positive integers such that
.




![\[ a_{n+2} = ka_{n+1} + a_n \]](http://latex.artofproblemsolving.com/b/5/e/b5e3e6f9f0b0709113498266e41b372299a2986f.png)



Summer is a great time to explore cool problems to keep your skills sharp! Schedule a class today!
Something appears to not have loaded correctly.