Archive for December, 2010

Attack of the Xmas murloc!

Sunday, December 26th, 2010

Geek joke for kids

Thursday, December 9th, 2010

Q. Why can’t you tell a joke in octal?

A. Because 7 10 11!

A maths diversion

Thursday, December 9th, 2010

One of my colleagues came into my office the other day, and said to me:

If p is prime and greater than 3, prove that p² – 1 is divisible by 24.

Interested readers might want to try this for themselves: it’s not particularly difficult. Of course I started in right away.

Immediately I thought: well, divisibility by 24 means divisibility by 2, by 3 and by 4. Let’s see what we can say about this considering p is odd. i.e. p = 2n + 1. So p² – 1 = (2n + 1)(2n + 1) – 1 = 4n² + 4n. Clearly divisible by 4.

Then I thought: aha. p² – 1 = (p + 1)(p – 1). One of (p + 1), p, (p – 1) is clearly divisible by 3, since these are 3 consecutive numbers. Since p is prime, either (p + 1) or (p – 1) is divisible by 3. Since p is odd, (p + 1) and (p – 1) are both even. And furthermore, since they are consecutive even numbers, one of them must be divisible by 4.

QED.

War is over if you want it

Thursday, December 9th, 2010

Indeed. Imagine what a better place the world would be if John had been alive these last 30 years. Have a happy and peaceful holiday season, whatever you celebrate.