# Math problem?

• Jan 4th 2009, 10:56 PM
EPark
Math problem?
Let n be a positive integer. Show that K=2^(2n-1)-9n^2+21n-14 is a multiple of 27.

To try to attempt solving this, I actually used a trial and error method where I plugged in various numbers just to see what I got. For instance, I did K(1), K(2), and K(3), but my answers were just 0. I'm sure there's an algebraic approach to this, but I need some guidance.
• Jan 4th 2009, 11:10 PM
Moo
Hello,
Quote:

Originally Posted by EPark
Let n be a positive integer. Show that K=2^(2n-1)-9n^2+21n-14 is a multiple of 27.

To try to attempt solving this, I actually used a trial and error method where I plugged in various numbers just to see what I got. For instance, I did K(1), K(2), and K(3), but my answers were just 0. I'm sure there's an algebraic approach to this, but I need some guidance.

And 0 is a multiple of 27 (Wink)

What you can do is a proof by induction, (supposing it's true for n, and checking for n+1)
I haven't thought of another way yet.
• Jan 5th 2009, 02:02 AM
craig
Yeh the method I would use here would be proof by induction, assuming true for n, making it equal to 27a, and then trying for n+1.

As moo stated though, 0 is a multiple of 27 ;)