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 \(n\). \(\blacksquare\)
–
Jubayer Nirjhor
·
3 years, 8 months ago

## Comments

Sort by:

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, 8 months ago

Log in to reply