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Homework Statement
(-8)^4124 + 6^3101 + 7^5 is divided by 3.
Homework Equations
The Attempt at a Solution
My original insight was that 6 raised to any power is always divisible by 3.
7 raised to any power yields a remainder of 1 when divided by 3.
and the remainder from -8 raised to a power alters from -2 (when exponent is odd) to 1 (when exponent is even.
So in my problem the first term leaves a remainder 1, the 2nd term no remainder and the final term remainder 1. What I am confused by, is how is this all effected when we add the numbers? My immediate intuition would tell me to add the remainders but I am sure that is incorrect.