Given any set of seven integers, must there be at least two that have the same remainder when divided by 6? To answer this question, let A be the set of 7 distinct integers and let B be the set of all possible remainders that can be obtained when an integer is divided by 6, which means that B has elements. Hence, if a function is constructed from A to B that relates each of the integers in A to its remainder, then by the pigeonhole principle, the function is not one-to-one . Therefore, for the set of integers in A, it is impossible for all the integers to have different remainders when divided by 6. So, the answer to the question is yes . (b) Given any set of seven integers, must there be at least two that have the same remainder when divided by 8? If the answer is yes, enter YES. If the answer is no, enter a list of seven integers, no two of which have the same remainder when divided by 8. {}