For a finite non empty set of primes P, let m(P) denote the largest possible number of consecutive positive integers, each of which is divisible by at least one member of P.(i) Show that ∣P∣≤m(P), with equality if and only if min(P)>∣P∣.(ii) Show that m(P)<(∣P∣+1)(2∣P∣−1).(The number ∣P∣ is the size of set P)Dan Schwarz, Romania inductionmodular arithmeticcombinatorics proposedcombinatorics