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#1 2007-12-21 00:32:41
- tony123
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- Registered: 2007-08-03
- Posts: 230
is an integer
prove
is an integer
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#2 2007-12-21 06:14:37
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
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 a[sub]n[/sub] is a sequence of integers and the formula for a[sub]n[/sub] is
In particular, a[sub]2008[/sub] is an integer
Last edited by JaneFairfax (2007-12-21 06:25:42)
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#3 2007-12-21 21:04:57
- tony123
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- Registered: 2007-08-03
- Posts: 230
Re: is an integer
JaneFairfax
wonderful solution
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