Question 27
An ordered pair of integers $(m, n)$ with $1 \lt m \lt n$ 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.
a. Find three Benelux couples $(m, n)$ with $m \leqslant 14$.
b. Prove that there exist infinitely many Benelux couples.