A number theory problem by Luke Tan

Number Theory Level 3

Is the number 1000C500 (1000 choose 500) divisible by 7?

I dunno No There's no way to tell Yes

Luke Tan by Luke Tan , 30, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Mathh Mathh
Aug 26, 2014

Just calculate ∑ k = 1 ∞ ⌊ 1000 7 k ⌋ − 2 ∑ k = 1 ∞ ⌊ 500 7 k ⌋ = 0 \sum_{k=1}^{\infty}\lfloor {\frac{1000}{7^k}} \rfloor - 2\sum_{k=1}^{\infty}\lfloor {\frac{500}{7^k}} \rfloor=0 .

You can easily do this by hand or you can use Wolfram Alpha .

2 Helpful 0 Interesting 0 Brilliant 1 Confused

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...