The conversation between human and AI assistant.
Prove that among any K consecutive integers, there is exactly one multiple of K?
Could you explain to me how to prove that among any K consecutive integers, there is exactly one multiple of K?
Sure! One way to prove this is by contradiction. Assume that there are no multiples of K in a sequence of K consecutive integers. Then, the remainders when each integer is divided by K must be distinct and range from 0 to K-1. But since there are only K possible remainders, this contradicts the fact that there are K consecutive integers.