Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

prove

is an integer

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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)*

Offline

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

JaneFairfax

wonderful solution

Offline

Pages: **1**