Question

If 'a' and 'b' are two positive integers greater than 20172017 and b – a > 4034, then there exist at least one pair a,
b such that the product (a –2017)(b+2017) is greater than the product (a + 2017)(b – 2017). (True/False)

Answer 1

Represent a,b,c in terms of their prime factors. Then D is the product of all the common prime factors, each factor taken as often as it appears the least number of times in a or b or c. M is the product of all the non-common prime factors, each factor taken as often as it appears the greatest number of times in a of b or c.

Therefore, MD may be less than abc, but it cannot exceed abc.

Obviously, MD equals abc when there are no common factors.