a) Find all positive integers $g$ with the following property: for each odd prime number $p$ there exists a positive integer $n$ such that $p$ divides the two integers

$$g^{n}-n \text { and } g^{n+1}-(n+1)$$

b) Find all positive integers $g$ with the following property: for each odd prime number $p$ there exists a positive integer $n$ such that $p$ divides the two integers

$$g^{n}-n^{2} \text { and } g^{n+1}-(n+1)^{2}$$