The set of numbers $(p, a, b, c)$ of positive integers is called [i]Sozopolian[/i] when: 

[b]* [/b]p is an odd prime number 

[b]*[/b] $a$, $b$ and $c$ are different and 

[b]*[/b] $ab + 1$, $bc + 1$ and $ca + 1$ are a multiple of  $p$. 

          a) Prove that each [i]Sozopolian[/i] set satisfies the inequality   $p+2 \leq \frac{a+b+c}{3}$

          b) Find all numbers $p$ for which there exist a [i]Sozopolian[/i] set for which the equality of the upper inequation is met.