andythemonster

3^1, the unit digit is 3; 3^2, the unit digit is 9; 3^3, the unit digit is 7; 3^4, the unit digit is 1; 3^5, the unit digit is 3 again; .... since that repeats every 4, the unit digit of 3^82 must be 9; so, the remainder must be 4.