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#1 2007-12-21 00:32:41

tony123
Member
Registered: 2007-08-03
Posts: 189

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. Let’s 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; I’ll 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
Member
Registered: 2007-08-03
Posts: 189

Re: is an integer

JaneFairfax
wonderful solution

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