October 7th, 2013, 08:30 AM  #1 
Newbie Joined: Sep 2012 Posts: 25 Thanks: 0  prime number
p and p^2 + 2 are prime numbers. prove that p^3 + 2 is prime number too. 
October 7th, 2013, 09:59 AM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: prime number
The only way for to be a prime number is if is divisible by 3, since if it was not divisible by 3, it would be equivalent to 1 mod 3 and then would be divisible by 3, hence showing that it is not prime. But if is divisible by 3, then p = 3 since p is prime and we have , which is prime.

October 7th, 2013, 10:01 AM  #3 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Re: prime number
Try looking at this mod 3.

October 7th, 2013, 10:29 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,851 Thanks: 1075 Math Focus: Elementary mathematics and beyond  Re: prime number
pē + 2 = (p  1)(p + 1) + 3. All primes greater than 3 are of the form 6n  1 or 6n + 1, hence pē + 2 is prime only when p = 3.

October 7th, 2013, 11:29 AM  #5 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Re: prime number
I was trying for a subtle hint, though it wasn't that subtle...


Tags 
number, prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A prime number  Dacu  Number Theory  3  March 27th, 2014 07:40 AM 
Prime Number  yo79  Math Events  3  February 22nd, 2013 12:45 PM 
prime number  fantom.1040  Algebra  2  June 29th, 2011 03:46 PM 
Prime Number  xfaisalx  Number Theory  15  July 6th, 2010 03:32 AM 
Looking for a certain Prime number  dancer42  Number Theory  5  March 18th, 2008 02:42 PM 