Question 2
a) Let $a\ne b$, $b\ne c$, $c\ne a$ and $abc\ne0$. Calculate $\frac1a+\frac1b+\frac1c$, given that $a(a-b)=b(b-c)=c(c-a)$.
b) Positive integers $a,b,c$ satisfy $a+b=b(a-c)$, where $c+1$ is the square of a prime number. Prove that at least one of $a+b$ and $ab$ is a perfect square.
b) Positive integers $a,b,c$ satisfy $a+b=b(a-c)$, where $c+1$ is the square of a prime number. Prove that at least one of $a+b$ and $ab$ is a perfect square.