Suppose that the set [unparseable or potentially dangerous latex formula] has been partitioned into disjoint pairs [unparseable or potentially dangerous latex formula] so that for all [unparseable or potentially dangerous latex formula] equals [unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]. Prove that the sum
[unparseable or potentially dangerous latex formula]
ends in the digit [unparseable or potentially dangerous latex formula]