2019 AMC 10C Problems/Problem 15

The problem is asking for 2019 to the power of 2019, 2019 times so lets find the remainder when 2019^2019 is divided by 7 we know that the modulos repeat so we can use fermats little therom 2019^6 has a remainder of 1 when divided by 7. Now we can easily figure out the remainder when 2019^2019 is divided by 7 we have to figure out the remainder when 2019 is divided by 6 because the remianders repeat after every 6 terms and we get that it is congruent to 3(mod 6) so we have to figure out the remainder when 2019^3 is divided by 7. 2019 is congruent to 3(mod7) 2019^3 is congruent to 6 mod 7 so the answer is 6 which is E.

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