Let A be a set of positive integers satisfying the following properties:
(i) if m and n belong to A, then m+n belong to A;
(ii) there is no prime number that divides all elements of A.(a) Suppose n1 and n2 are two integers belonging to A such that n2−n1>1. Show that you can find two integers m1 and m2 in A such that 0<m2−m1<n2−n1
(b) Hence show that there are two consecutive integers belonging to A.
(c) Let n0 and n0+1 be two consecutive integers belonging to A. Show that if n≥n02 then n belongs to A. number theory unsolvednumber theory