help!

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.

That is pretty ingenious and is better than what I did!

333^333 mod 33 = 27

333^1 mod 33 = 3

333^2 mod 33 = 9

333^3 mod 33 =27

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333^8 mod 33 =27

333^333 mod 33 = 27