Question 32
The positive integers $a \lt b \lt c$ are such that $a + b + 2c$ is a common multiple of $b$ and $c$ (*).
a) Prove that the greatest common divisor of $a + b$ and $c$ is $c$.
b) Find the positive integers $k \lt 1000$, so that $abc = k^2$ and $a, b, c$ fulfill (*).
a) Prove that the greatest common divisor of $a + b$ and $c$ is $c$.
b) Find the positive integers $k \lt 1000$, so that $abc = k^2$ and $a, b, c$ fulfill (*).