y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that P = (x - y1 ) (x - y2 ) (x - y3) .... up to infinity, where x is an integer. Which of the following value can x take so that p has the least value?
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III
not sure i got it properly.
what is the possible least value of p if it is not -ve? 0.
when is p = 0? if any of (x - y1 ) or (x - y2 ) or (x - y3) is 0.
so if one of either y1 or y2 or y3 is 1, then x has to be -1 so that p becoms 0.
similarly, if y1 or y2 or y3 is -1, then x has to be 1 to make p = 0.
if any of y1 or y2 or y3 is 0, then x has to be 0, then only p becomes 0.
so for me E.