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⩽14.
(b) Prove that there are infinitely many Benelux couples number theory proposednumber theory