Question 2
$a$)Pairwise distinct nonzero $a , b , c$ satisfy $a \left(a - b\right) = b \left(b - c\right) = c \left(c - a\right)$. Find $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$. $b$)Positive integers satisfy $a + b = b \left(a - c\right)$ and $c + 1 = p^{2}$ for a prime $p$. Prove $a + b$ or $ab$ is a square.