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- Feb 13th 2007, 07:31 PMchillerbros17Proof of checkerboard pieces
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- Feb 13th 2007, 09:25 PMCaptainBlack
- Feb 13th 2007, 09:35 PMCaptainBlack
6. Prove the following theorems. State the method of proof that you are using in parts (a) and (c).

(a):Thm: The sum of two prime numbers, each greater than 2, is never a prime. Restatement: For all integers p, q, if p is a prime greater than 2 and q is a prime greater than 2, then p + q is not prime.

Proof by Contradiction (Reductio ad absurdum)

If p and q are primes greater than 2, then p and q are both odd, and may

be written p=2a+1, q=2b+1, for some positive integers a, and b.

Now suppose p+q is prime, then as it is greater than 2, it must be odd.

But:

p+q=2a+1+2b+1=2(a+b+1).

Thus p+q is divisible by 2, and hence not prime (as p+q !=2), which

is a contradiction, hence our assumption is false, and p+q is not prime.

RonL - Feb 14th 2007, 07:51 AMchillerbros17
Attachment 1724

Here's is b with the right pattern. Sorry for the mistake. - Feb 14th 2007, 12:11 PMCaptainBlack