MathDB

6. Prove or disprove the following two propositions: (i) If

a

and

b

are positive integers such that

a<b

, then in any set of

b

consecutive integers there are two whose product is divisible by

ab

(ii) If

a,b

and

c

are positive integers such that

a<b<c

, then in any set of

c

consecutive integers there are three whose product is divisible by

abc

. (N.8)

6