It's part of a larger problem but this is what I got left; if
3^a - 2^a is a prime number, then a is a prime number. If anyone
could point me to the right direction to prove/disprove this, it
would be nice. Thanks! I do not know if i am going to help you,
but: Why dont you try to expand the identity as follow: From
binomial expansion we have: And then we have the equality: From
there i have nothing more... If we rise both sides to a expand
the right side and the again rise to a, mayby we could compare
the addition terms. if we try to simplify left side by divisions
of 2. again i do not know if this helps to prove (or disprove)
your identity. So you need to show that: If is NOT a prime
number, then is NOT a prime number. Recall that a prime number
is one that only has 1 and itself as factors. So to show that is
not prime, we would have to show that it has a common factor.
First, if is not prime, then it can be expressed as , where .
Now we make use of the factorisation rule Thus is not prime. So,
if is not pri