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Discrete Math help

 

02-12-14 09:34 PM
OracleofthePenguin is Offline
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The question is:  ForAll integers a, b; a>2 implies (a does not divide b) or (a does not divide b+1)
So basically, a either can't divide a number or the number after that one.

I don't even know where to start! Any help would be greatly appreciated. ^w^

Bonus Question!
Prove that the sum of two odd primes is never prime.
The question is:  ForAll integers a, b; a>2 implies (a does not divide b) or (a does not divide b+1)
So basically, a either can't divide a number or the number after that one.

I don't even know where to start! Any help would be greatly appreciated. ^w^

Bonus Question!
Prove that the sum of two odd primes is never prime.


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02-12-14 10:22 PM
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I am a biologist slash weather forecaster. Geez math has sure changed since I was in grade school. 

Okay what you want to do is use the simple definition of a prime number to help solve your problem. Assuming A is the prime number in your problem. A cannot be divided by b or it can't be divided by b plus one. 

For the bonus question 
look up Goldbach's conjuncture 
I am a biologist slash weather forecaster. Geez math has sure changed since I was in grade school. 

Okay what you want to do is use the simple definition of a prime number to help solve your problem. Assuming A is the prime number in your problem. A cannot be divided by b or it can't be divided by b plus one. 

For the bonus question 
look up Goldbach's conjuncture 

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02-13-14 09:16 AM
OracleofthePenguin is Offline
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I don't understand..."a" isn't necessarily a prime number. For example, if "a" is 5 and "b" 30, "a" does divide 30 but it does not divide 31. I have to prove that this is true for all integers "a" greater than 2.
I don't understand..."a" isn't necessarily a prime number. For example, if "a" is 5 and "b" 30, "a" does divide 30 but it does not divide 31. I have to prove that this is true for all integers "a" greater than 2.

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02-23-14 09:27 AM
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I don't take discrete math, but I think I've got the bonus.

Bonus:
If the result even, then it's not prime, since it's divisible by two.

Let x = any odd prime
Let y = any odd prime

Since, odd + odd = even, then x + y = z, where z is even.

If the sum of two prime numbers isn't always prime, then z would be prime in at least one case.

Since z is even, it's always divisible by two, meaning that the sum of two primes is never prime, (1 cannot be substituted for x or y, since it's not prime of course).
I don't take discrete math, but I think I've got the bonus.

Bonus:
If the result even, then it's not prime, since it's divisible by two.

Let x = any odd prime
Let y = any odd prime

Since, odd + odd = even, then x + y = z, where z is even.

If the sum of two prime numbers isn't always prime, then z would be prime in at least one case.

Since z is even, it's always divisible by two, meaning that the sum of two primes is never prime, (1 cannot be substituted for x or y, since it's not prime of course).

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(edited by EideticMemory on 02-23-14 01:58 PM)    

02-23-14 07:31 PM
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Thanks for the responses! I've handed in the homework so you can close this topic now. :3
Thanks for the responses! I've handed in the homework so you can close this topic now. :3

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(edited by OracleofthePenguin on 02-23-14 07:33 PM)    

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