Problem $1(3+5=8)$ What does this code do$?$

You encounter the following mysterious piece of code.

$($a$)$ What are the results of $F(a,3),F(a,4),$ and $F(a,5).$ You do not need to justify your answers.

$($b$)$ What does the code do in general, when given input integer $n0?$ Prove your assertion by induction

on $n.$