Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Lucas Number Questions

1) Find (a,b) such that

Where n is the nth lucas number.

How would I start this? Would I just start by plugging in a=b=1a=b=1 and then trying to solve?

Last edited by Oran2009 (2017-04-02 01:50:54)

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Lucas Number Questions

No, because

and

are the things you are trying to find. We already know that

and

. So take

and

to get two different linear equations in

and

which you should be able to solve. You should get

assuming that by

you mean

. Then once you've found your formula, prove it by induction on

.

Last edited by zetafunc (2017-04-02 02:20:58)