Suppose we have \(n\in \mathbb{N}\) with \(m\) digits. Now consider the number, \[\]\[\large{A=123456789\underbrace{000...000}_{(m+1)~\text{zeros}}}\]\[\]So exactly one \(N\in \left\{A+1, A+2, ... , A+n\right\}\) must be a multiple of \(n\). \(\blacksquare\)
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Jubayer Nirjhor
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3 years, 4 months ago

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TopNewestSuppose we have \(n\in \mathbb{N}\) with \(m\) digits. Now consider the number, \[\]\[\large{A=123456789\underbrace{000...000}_{(m+1)~\text{zeros}}}\]\[\]So exactly one \(N\in \left\{A+1, A+2, ... , A+n\right\}\) must be a multiple of \(n\). \(\blacksquare\) – Jubayer Nirjhor · 3 years, 4 months ago

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