Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2007-12-21 23:32:41

tony123
Full Member

Offline

is an integer

prove



is an integer

 

#2 2007-12-22 05:14:37

JaneFairfax
Legendary Member

Offline

Re: is an integer

Construct a recurrence sequence of integers for which that number is the 2008th term. Lets see



are roots of the quadratic equation



This would be the characteristic equation of the recurrence relation



Choose



and



which should be an integer. Is it? I think so anyway; Ill leave you to check. So an is a sequence of integers and the formula for an is



In particular, a2008 is an integer

Last edited by JaneFairfax (2007-12-22 05:25:42)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#3 2007-12-22 20:04:57

tony123
Full Member

Offline

Re: is an integer

JaneFairfax
wonderful solution

 

Board footer

Powered by FluxBB