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#1 2017-04-02 01:50:13

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)

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#2 2017-04-02 02:18:51

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
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)

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