The conversation between human and AI assistant.
Prove that among any K consecutive integers, there is exactly one multiple of K?
That makes sense. Are there any other ways to prove it?
Another way is by using the pigeonhole principle. Let's assume that there are no multiples of K in a sequence of K consecutive integers. Then, we can use the remainders when each integer is divided by K to separate the integers into K boxes. Since there are K integers and K boxes, at least one box must have two or more integers in it. But if one box has two integers, then their difference must be a multiple of K, which contradicts the assumption that there are no multiples of K in the sequence.