- #1
bloynoys
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Homework Statement
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.
Homework Equations
For both, assume the contradiction work towards finding it is impossible.
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?