"Jeremy Boden" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Fri, 2006-08-18 at 14:34 +0000, AB wrote: >> Jeremy Boden wrote: > ... >> > On the basis that 1 is neither a prime, nor a non-prime number:- >> 1 is definitely not prime. > > In order to avoid a pointless/endless controversy about whether 1 is > prime or not, I will restate my original question! > > Prove that (for n >= 12) n can be written as the sum of two different > numbers which are:- > a) Different and > b) Not prime and > c) Not = 1 > > How long should I expect a reasonably able high-school child to take to > solve this? I'm trying to invent some "simple to state" and do-able > homework for my son during the long school holiday.
After few minutes considering I offer this solution:
1) Even numbers>12 equals to the sum of 4+some even number. 4 is not prime neither even number>=4. Examples: 4+4=8, 4+6=10, 4+8=12 etc. Generally 8+2x, where x is some positive integer >=0. 2) Odd numbers>12. You do not accept 1. Further 2,3,5,7 are primes thus the first odd, which is not prime is 9 - as you want omit 1. Thus any odd n>12 is the sum 9+even, which is greater than 2, at least 4. For example 9+4=13, 9+6=15, 9+8=17 etc. Generally 9+2*y, where y is some positive integer>=2. Well, your homework for your son is OK.