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 \(y\).)

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