# Homework Help: Prove or disprove, induction

1. Dec 8, 2008

### mbcsantin

1. The problem statement, all variables and given/known data

For all n is an element of N, n2 - n + 41 is prime
N= natural numbers

2. Relevant equations

None.

3. The attempt at a solution

Let n=1
12 - 1 + 41 = 41 is prime.

n2 - n + 41 is not prime. so this hypothesis is not correct.
assume n2 - n + 41 is not prime. there exist n that let n2 - n + 41 = n2 so n2 - n + 41 is not prime.
therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n2 - n + 41 is not prime.
Hence n2 - n + 41 not true for all n is an element of N.

2. Dec 8, 2008

### mutton

You have the right idea, that when n = 41, n^2 - n + 41 is not prime.

Your proof doesn't make sense though. You can't begin by assuming the intended conclusion. It's not clear why there exists an n such that n^2 - n + 41 = n^2 and that this number is not prime. Work on articulating what you mean.

3. Dec 8, 2008

### HallsofIvy

That's not supposed to be a "proof" of anything. It's a perfectly valid way of finding a counter example to the supposed theorem. The "proof" that the theorem is false is simply asserting that if n= 41, n^2- n+ 41= 41^2 is NOT prime. How you got to n= 41 is not relevant to the proof.