Waste less time on Facebook — follow Brilliant.

digits 0-9 in a multiple of any integer

Prove that every positive integer has a multiple whose decimal representation involves all ten digits.

Note by Sarath Ch
3 years, 8 months ago

No vote yet
1 vote


Sort by:

Top Newest

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

Log in to reply


Problem Loading...

Note Loading...

Set Loading...