It's so annoying, it was fun watching the answer come out the same every time...I even did it for a 30x30 matrix...

In the maths department last year, my supervisor was president of the Maths Society and there's this guy who I shall name PBIG(Proof By Induction Guy, it's what I call him) who is possibly the most annoying person ever...and he drives everyone mad...

Anyway, he was trying to prove everything by induction(Fermat's Last Theorem included), proof by induction being where you prove a statement is true for n=1 and then assume it's true up to n=k then use that to prove it's true for n=k+1, from that you can deduce it's true for all n.

And he came up to Goldbach's conjecture which states that every even number can be written as the sum of two primes, and when he came to the induction step(assuming n=k bit) he basically assumed Goldbach's conjecture and that for the primes that sum to an even number, one must be a prime double(ie. the primes have a difference of 2, eg. 17, 19) and the number in the sum must be smaller than the other prime.

Now the first counterexample to this is 38 = 31+7...and at the pub they continued to find counterexamples...and eventually they went home...and whilst drunk, my supervisor's friend(if you watched G103 when I posted it, the main character in that) saw that there was a pattern in these counterexamples and that all counterexamples to PBIG's conjecture(the prime double sum stuff) is of the form 38+6n, where n is a whole positive number.

This escalated and my supervisor was working with someone in the Maths Department to write algorithms to see whether or not it held, and they managed to get it so that they showed that that was true for the first 10 billion numbers of that form...of course they modified it slightly and it sort of linked Goldbach's conjecture with the Twin Primes conjecture(There are an infinite number of twin primes)...

It was all very interesting but I think it came to naught at the end because the guy who'd agreed to help had the mickey taken out of him for working with undergraduates...and things just tailed off...I don't know what happened...

But during the entire thing PBIG was a right t**t about it...he contributed nothing to it but a conjecture that was false and he wanted recognition for that...he drove my supervisor up the wall...