Question 55
a) Prove that $7$ cannot be written as a sum of squares of three rational numbers.
b) Let $a$ be a rational number that can be written as a sum of squares of three rational numbers. Prove that $a^m$ can be written as a sum of squares of three rational numbers, for any positive integer $m$.
b) Let $a$ be a rational number that can be written as a sum of squares of three rational numbers. Prove that $a^m$ can be written as a sum of squares of three rational numbers, for any positive integer $m$.