Anyone good with proofs? math
The question im working on here is...
This problem involves prime numbers. A number p is called prime if it is a natural number (i.e.
positive integer) such that the only integers that divide it without remainder are 1; 1; p; and p.
Examples of primes include 2; 3; 5; 7; 11; :::. The number 1 is NOT prime. Also, note that 2 is the only
even prime number (make sure you understand why).
Consider the following statement. If it is true, prove it. If it is false, fi nd a counterexample.
Let p be a prime number.
Then the number p^2 + p + 2 is not prime.
I have to prove it if its true or provide a counterexample if false.
I am kind of hopeless with proofs here and any help would be great so I can finally be done with this homework!E
EDIT: wrote it wrong, its fixed.
2 Comments • Newest first
[quote=SwitcherUpper]Well, if it helps then that's good. I haven't done a proof in 7 years, and when our teacher explained them to us, he used Monty Python. Yea, I didn't learn anything in that class.[/quote]
haha yea this made sense now that I think about it. Just sort of in a rush to finish this problem before class so I dont have the time to really study the material better. Thanks again.
@above, thanks alot! I was writing it in cases but this might make it shorter
[quote=SwitcherUpper]I'm horrible with proofs, but I'm pretty sure that it is true.
My reasoning : If you use 2 as p, you will end up with an even number, 4 + 2 + 2 = 8. If you use any odd number, which the rest of the prime numbers are, when you add p to p^2 you will get an even number. Multiplying is like adding a number to itself a certain number of times. If you multiply an odd number(p) by itself (p^2), you will get another odd number. When you add two odd numbers together (p^2 + p) you will get an even number. Adding 2 will keep it even as well.
I don't know how to write it up correctly though.[/quote]
thanks! anything that gives me direction would be great.