a. Suppose a1,a2,...,an is a sequence of n integers none
Chapter 9, Problem 9.171(choose chapter or problem)
a. Suppose a1,a2,...,an is a sequence of n integers none of which is divisible by n. Show that at least one of the differences ai aj (for i = j) must be divisible by n. Show that every nite sequence x1,x2,...,xn of n integers has a consecutive subsequence xi+1,xi+2,...,xj whose sum is divisible by n. (For instance, the sequence 3, 4, 17, 7, 16 has the consecutive subsequence 17, 7, 16 whose sum is divisible by 5.) (From: James E. Schultz and William F. Burger, An Approach to Using Equivalence Classes Modulo n, College Mathematics Journal (15), No. 5, 1984, 401405.)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer