I've got this problem and have no idea how to start. Please, could anyone give me a hint?
Let be positive integers and define . Prove that not all the can be primes.
Thanks for replying.
Working out the general term I've seen it can be written this way:
I don't know if it's the more suitable for the exercise.
Now, do you tell me to suppose ? or, is p just a prime that is not related to the sequence?
Yes so either they are all composite in which case we are done, or there is one, , that is a prime p say. Then for all r. This uses the fact that (a,b)=1 and
So they can't all be primes.
(I believe that is enough to show they can't all be primes?)