logical proof problem

[Kagey]

Hey all,,

This is my first post in the math forum, and probably not my last.

I am working on a discrete math structures assignment, and am having a little bit of a problem understanding some aspects of logical proofs. the methods we have covered are: induction, contradiction, indirect, and counter example.

the question i am having trouble with is:
prove:
n^2 + 41n + 41 is prime for every int n.

I know that it is true, but how the heck do i prove it?

[Lior]

Originally posted by Kagey

I know that it is true, but how the heck do i prove it?

Well, I don't wanna let you down, but this "theorem" is just false!

For N=4 the whole expression equals to 221 which is not prime!
(221=17*13)

That simple.

[DavidHooper]

Lior speaks the truth.

[Lior]

Thanks David,

By the way, when do you start your semester at Cambridge University ?

[DavidHooper]

October 5th, for fresher's week. Can't wait!

[Lior]

I wish you luck.

By the way, Kagey, If I'm not mistaken, the world hasn't found yet an expression which always generates a prime number.

[Kagey]

ok thanks guys, i also figured out that when n = 6 it doesnt work either. I think i should try the obvious from now on eh.

[sql_lall]

for some reason i recall a book saying it worked up to 39, but i must check it.

The most obvious reason why it is wrong: use n = 41
41² + 41² +41
= 41(83) = not prime (easy to see 41 is a factor from above)