Prove that random variable has exponential distribution

Question

I have a non-negative continuous random variable $X$ and I am given $P(x>a+b)=P(x>a)P(x>b)$. I need to prove that the probability distribution is exponential. I already know that $F(x)=0$ if $x \leq 0$ where $F(x)=P(X \leq x)$ so I should be able to show that otherwise $F(x)=1- \exp(-ax)$ for some constant a.