Primes Question - AMTI Inter Level Finals

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

Find the sets of primes xx, yy and zz that satisfy the condition above. Submit your answer as the sum of all possible values of xx, yy and zz.

Note: If all the possible solutions are, for example, (3,4,5)(3, 4, 5), (5,12,13)(5, 12, 13) and (9,12,15)(9, 12, 15), then the sum will be 3+4+5+5+12+13+9+153+4+5 + 5+12+13 + 9+15. (The last 12 is omitted since yy only has two possible values; 5 still appears twice since it appears for different variables xx and yy.)

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