An ordered pair of integers $(m, n)$ with $1<m<n$ is said to be a Benelux couple if the following two conditions hold: $m$ has the same prime divisors as $n$, and $m+1$ has the same prime divisors as $n+1$. (a) Find three Benelux couples $(m, n)$ with $m \leqslant 14$. (b) Prove that there exist infinitely many Benelux couples.