[ prime numbers and their properties $]$

It is known that $p>3$ and $p-$ is a prime number.

a) Do you think at least one of the numbers $p+1$ and $p-1$ will be divisible by 4?

b) And by 5?
a) Consider the numbers $p-1, p, p+1, p+2$. Among four consecutive numbers, one is definitely divisible by 4, but it is not $p$ and not $p+2$ (both these numbers are odd). Therefore, one of the numbers $p+1$ or $p-1$ will be divisible by 4.

b) For example, when $p=13$, neither of these numbers is divisible by 5.

## Answer

a) It will; b) not necessarily.