Quandaries
and Queries
HI
My name is Antonio .
I am a secondary student .I have difficulties in proving the following:
The numbers p and 8p2 +1 are prime. Prove that the number 8p2+2p+1 is also a prime number.
Thanks for your help.
Hi Antonio,
If p = 3 then 8p2 +1 = 73 which is a prime and 8p2+2p+1 = 79 which is also a prime.
If p is a prime that is not 3 then division of p by 3 leaves a remainder of either 1 or 2.
If the remainder after dividing p by 3 is 1, then the remainder after dividing p2 by 3 is also 1. Thus the remainder after dividing 8p2 +1 by 3 is 0, and hence 8p2 +1 is not a prime.
What can you say if the remainder after dividing p by 3 is 2?
Claude and Penny