## Friday, October 21, 2005

### Help needed with my homework

Exciting morning today. Had a whole 2 hours of work on prime numbers, which included a proof that there are an infinite amount of primes. Then had a hard worksheet on primes. Got stuck on one question so here's something for you to ponder (This is for you Dad) :

1. Prove that every integer of the form 4k+3 has a prime factor of that form.

Correct answers are very much appreciated!

Quite excited at the moment cos I've just copied someones copy of Switchfoot's new album to my computer. Am looking forward to turning it up loud later. Feeling a bit guilty though cos it had been on my xmas list, so I probably don't need it anymore. (Hope mum and dad haven't bought it yet!!!)

And in other Chrstn rock news, Delirious reached no. 56 in the charts on Sunday. Bit disappointing.
Hey, you can always rely on me to satisfy your Chrstn music and maths needs.

Anonymous said...

This problem is sooooo easy bruv.
You can say that I = -1 mod 4
I standing for integer. Either I is prime or composite. If prime, than it is divisible by itself i.e. divisible by a number of the form 4k+3. If composite, that number must be the product of at least 2 prime numbers. It cannot be divisble by 2 being odd. Hence it must be divisible by an odd number. If it were only divisible by odd numbers of the form 4k+1 or P (prime)= 1 mod 4, then when you multiply them, you never get -1 mod 4 only 1 mod 4. ( see rules of mods). Hence, this integer 4k+3 must be divisible by at least one prime of the same form.
:-)

Anonymous said...

sorry bruv, that aint that clear because the I looks like a 1. Hope you still get it.