Question 63
Suppose that for two natural numbers $m, n$ the following equality holds
$$
m+n = [m,n] + (m,n),
$$
Where $[m,n]$ and $(m,n)$ are the least common multiple and the greatest common divisor of $m,n$ respectively. Prove that one number is divisible by another.
$$
m+n = [m,n] + (m,n),
$$
Where $[m,n]$ and $(m,n)$ are the least common multiple and the greatest common divisor of $m,n$ respectively. Prove that one number is divisible by another.