Digits!

Find the unit digit in 6535^458 - 5867^482


The answer is 4.

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

Bloons Qoth
Aug 13, 2016

653 5 458 586 7 482 6535^{458} - 5867^{482} , we'll use Modular Arithmetic to find the unit digit.

5 n 5^n where n n is any positive integer, its unit digit will result in a 5 5

So 653 5 458 5 458 5 ( m o d 10 ) 6535^{458} \equiv 5^{458} \equiv \boxed{5} \pmod{10}

586 7 482 7 482 4 9 241 9 241 ( 1 ) 240 ( 1 ) 1 1 9 ( m o d 10 ) 5867^{482} \equiv 7^{482} \equiv 49^{241} \equiv 9^{241} \equiv (-1)^{240} * (-1) \equiv 1 * -1 \equiv \boxed{9} \pmod{10}

5 9 = 4 5-9 = -4 , which implies 4 \color{#20A900}{\boxed{4}} is the last digit.

Moderator note:

As the value is negative, the last digit will be 4.

the second term is larger which makes the answer a negative integer: -2379877...214664

Bob Kadylo - 4 years, 9 months ago

Log in to reply

How can I guess as to which number is greater manually?

Ankit Kumar Jain - 3 years, 1 month ago

I fixed my mistake. Thanks...Aniket.

Bloons Qoth - 4 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...