Question 136
a. Prove that there exist infinitely many triples $(x, y, z)$ of positive integers such that $x^{2}+y^{2}+z^{2}$ is a perfect square.
b. Prove that there exist infinitely many triples $(x, y, z)$ of positive integers such that $x^{2}+y^{2}+z^{2}$ is a perfect square and with the property that the greatest common divisor of the three numbers $(x, y, z)$ is 1.
b. Prove that there exist infinitely many triples $(x, y, z)$ of positive integers such that $x^{2}+y^{2}+z^{2}$ is a perfect square and with the property that the greatest common divisor of the three numbers $(x, y, z)$ is 1.