National Olympiad Final Round

If numbers $a$ and $a+735$ had exactly $2$ divisors, they would be primes. These numbers are of different parity, whence one of them is even. But if $a=2$ then $a+735=737=11\cdot 67$. If numbers $a$ and $a+735$ had exactly $3$ divisors, each of them would be a square of a prime. Similarly to the previous case, we get $a=4$. But then $a+735=739$, and $739$ is not a perfect square. On the other hand, numbers $10$ and $10+735$ have exactly $4$ divisors.