Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Easy problem (Opposite of Goldbach???)
Replies: 23   Last Post: Aug 24, 2006 6:56 PM

 Messages: [ Previous | Next ]
 Tapio Hurme Posts: 853 Registered: 12/8/04
Re: Easy problem (Opposite of Goldbach???)
Posted: Aug 18, 2006 4:23 PM

"Jeremy Boden" <jeremy@jboden.demon.co.uk> wrote in message
news:1155912652.7060.7.camel@localhost.localdomain...
> 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.

Tapio

>
> --
> Jeremy Boden
>
>

Date Subject Author
8/18/06 Jeremy Boden
8/18/06 AB
8/18/06 Jeremy Boden
8/18/06 AB
8/18/06 Jeremy Boden
8/18/06 mareg@mimosa.csv.warwick.ac.uk
8/18/06 Dik T. Winter
8/19/06 Phil Carmody
8/19/06 Jeremy Boden
8/19/06 Phil Carmody
8/18/06 Tapio Hurme
8/18/06 Jeremy Boden
8/19/06 Butch Malahide
8/19/06 Proginoskes
8/19/06 Virgil
8/22/06 T.H. Ray
8/23/06 Proginoskes
8/23/06 T.H. Ray
8/23/06 fernando revilla
8/23/06 Jeremy Boden
8/23/06 Tapio Hurme
8/23/06 T.H. Ray
8/24/06 Jeremy Boden
8/24/06 T.H. Ray