FIND ALL SOLUTIONS IN POSITIVE INTEGERS X, Y, Z TO THE SIMULTANEOUS...

2. Find all solutions in positive integers x, y, z to the simultaneous

required, with complete proofs of any assertions

equations

you may make. Marks awarded will depend on the

x + y − z = 12

clarity of your mathematical presentation. Work

in rough first, and then write up your best attempt.

x

2

+ y

2

− z

2

= 12.

Do not hand in rough work.