Random quote and an easy problem

"Guys have the romantic idea that you don’t poop. I doubt that shattering that dream would ruin an otherwise great relationship too terribly."

Hehe.

Anyway, I keep getting stumped by problems out of my books so I needed a breather. Here's an easier one that I quickly made up.

Prove that infinitely many of the Fibonacci numbers are multiples of 3

Really all you have to do is look at them mod 3:

1, 1, 2, 3, 5, 8, ....

In mod 3, goes:

1, 1, 2, 0, 2, 2, 1, 0, 1, 1, ....

And as you can see, this sequence repeats, making infinitely many numbers congruent to 0 mod 3.

It is now 5:51 in the AM. I really need to even out my schedule. And still no luck with that other problem. I haven't given up though.