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I have noticed two questions here and here which are nearly identical in nature. These questions ask to show that given any $n+1$ integers, there exist at least two integers whose difference is divisible by $n$. Should these questions be regarded as abstract duplicates? |
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The second question (with $n=2$) is a special case that may be worth keeping separate from the general case, since it only requires working with even and odd numbers. That makes the solution accessible to even elementary school students. Many students in my undergraduate number theory course, even after working with modular arithmetic for a few weeks, easily wrote proofs using even and odd numbers but did not see the straightforward generalization to integers modulo $n$ without prodding. One of them could be closed as a duplicate, but I see value in leaving both of them, along with your helpful link that connects them. |
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