Remainders

Number Theory Level 4

Let N = 122333444455555 ⋅ ⋅ ⋅ N = 122333444455555 \cdot \cdot \cdot , a 100 100 digit number . Find N ( m o d 16 ) N \pmod{16}

This is part of the set My Problems and THRILLER


The answer is 9.

Ankit Kumar Jain by Ankit Kumar Jain , 20, India

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

Till 9, there will be 45 digits. After writing ten 10s, well get 65 digits After writing eleven 11s, well get 87 digits. Next, we'll write twelve 12s, but. We have an even digit number. So, the number will end with 2121. Dividing this by 16, we get the required remainder, which is 9.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Arkodipto Dutta
Feb 3, 2016

same method

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...