# Primes Question - AMTI Inter Level Finals

$\large x(x+y)=z+120$

Find the sets of primes $x$, $y$ and $z$ that satisfy the condition above. Submit your answer as the sum of all possible values of $x$, $y$ and $z$.

Note: If all the possible solutions are, for example, $(3, 4, 5)$, $(5, 12, 13)$ and $(9, 12, 15)$, then the sum will be $3+4+5 + 5+12+13 + 9+15$. (The last 12 is omitted since $y$ only has two possible values; 5 still appears twice since it appears for different variables $x$ and $y$.)

×