Powers of 3

Number Theory Level 3

Find the minimum integer n > 1 n > 1 for which the last three digits of 3 n 3^n is 003.


The answer is 101.

Aditya Moger by Aditya Moger , 17, 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.

1 solution

Aditya Moger
Aug 13, 2017

We know that

3^n Mod 1000 = 3

Every n is of the form

100m+1 where m belongs to positive integers

n is minimum when m=1 Therefore

n = 100 * 1 + 1= 101

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Your solution doesn't show that the smallest possible value of "n" is 100.

How do you know that "n" cannot be less than 100? Did you test out the remaining 99 numbers?

Pi Han Goh - 3 years, 10 months ago

how did you know the every n is of the form 100m+1?

Dhrubajyoti Ghosh - 3 years, 10 months ago

Log in to reply

I esy to find. Try it u'll get it

Aditya Moger - 3 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...