I am trying to do a proof by contradiction question and i am stuck at stage 1:
How do i contradict this? It strikes me there are two options:
1. Suppose 4^n -1 is NOT prime when n is odd
2. Suppose 4^n-1 is prime when n is NOT odd ( i.e. even)
How do i know which contradiction to start with in this particular case? Or can this be proved by contradiction in two different ways and it doesn't matter?
With the two classic proofs by contradiction ( root 2 is irrational, infinite number of primes) it feels clear to me what the contradiction statement is, but with the one above it doesn't?
I don't want anyone to do the proof for me just to offer advice about how to contradict the statement. Thanks
How do i contradict this? It strikes me there are two options:
1. Suppose 4^n -1 is NOT prime when n is odd
2. Suppose 4^n-1 is prime when n is NOT odd ( i.e. even)
How do i know which contradiction to start with in this particular case? Or can this be proved by contradiction in two different ways and it doesn't matter?
With the two classic proofs by contradiction ( root 2 is irrational, infinite number of primes) it feels clear to me what the contradiction statement is, but with the one above it doesn't?
I don't want anyone to do the proof for me just to offer advice about how to contradict the statement. Thanks