+37 two problems of the same type:
what is the remainder of 7^2019/5?
what is the remainder of 333^333 / 33?
thanks
+2863 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.
+37 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!
