Good morning!

I have checked the following statement by random numbers of my choice. I am seriously looking for proof of the statement.

Statement: $m$ is said to be Fermat pseudo prime in base-3, when $m=ab$ with $a$ is some prime and $>3$ and $b$ is also prime and can be expressible in terms of $a$ (i.e., $b = 2a-1$).

Question(s): 1) can you prove the above statement? 2) can we extend the same for other bases like 4, 5, 6 etc?

High regards,

Thanks in advance.

BIT.Ganmurt