Reminding Remainders 2

Number Theory Level 3

What is the remainder when 100...(200 0's)...001 is divided by 1001?


The answer is 0.

Kenneth Gravamen by Kenneth Gravamen , 23, Philippines

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

Karan Pedja
May 26, 2015

10 3 ≡ − 1 ( m o d 1001 ) { 10 }^{ 3 }\equiv -1(mod\quad 1001) Therefore 10 201 ≡ 1 0 3 67 ≡ ( − 1 ) 67 ≡ − 1 ( m o d 1001 ) { 10 }^{ 201 }\equiv {10^{3}}^{67} \equiv {(-1)}^{67} \equiv-1(mod\quad 1001) So, finally 1 0 201 + 1 ≡ 0 ( m o d 1001 ) 10^{201}+1 \equiv 0 (mod 1001)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

11 11

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...