(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?

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# Proof by contradiction - polynomials and infinite primes

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