two problems of the same type:

what is the remainder of 7^2019/5?

what is the remainder of 333^333 / 33?

thanks

Starz Apr 28, 2019

#1**+4 **

**1. Simple pattern recognizing.**

Remainder of when divided by 5-

7^1=2

7^2=4

7^3=3

7^4=1

7^5=2

and so on

This means the remainder pattern is 2, 4, 3, 1,

To find the remainder of 7^2019, we find the remainder of 2019 divided by 4 because there are 4 terms in the pattern.

Since the remainder is 3, we count up 3 times in the pattern.

So the remainder of 7^2019 divided by 5 is **3.**

CalculatorUser Apr 28, 2019

#2**+1 **

Thanks! I wasn't sure if Modulo 7^2019 worked on this kind of problem, and yeah, I think it does.

So my way (that I didn't know that worked) was to see the ones digit for powers of the remainder of 7 mod 5.

2, 4, 8, 6

It would be 8, and then divide that by 5 and get the remainder of 3.

Thanks!

Starz
Apr 28, 2019