(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two Questions:

1. Prove, by contradiction, that if a and b are integers and b is odd,, then -1 is not a root of f(x)= ax^2+bx+a.

2. Prove, by contradiction, that there are infinitely many primes as follows. Assume that there only finite primes. Let P be the largest prime. Explain why there is a prime dividing P!+1 and find the the contradiction.

2. Relevant equations

For both, assume the contradiction work towards finding it is impossible.

3. The attempt at a solution

1. (x-1)(x-a)=ax^2+bx+a

Not sure where to go from there

2. This is not a normal infinite prime solutions as we have gone over a few of the solutions in class. I am not sure what she means by "there is a prime dividing P!+1" as that isn't really a clear sentence. Any Ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof by contradiction - polynomials and infinite primes

**Physics Forums | Science Articles, Homework Help, Discussion**