Question 111888
3^0 ___ 1 _____ R/7=1
3^1 ___ 3 _____ R/7=3
3^2 ___ 9 _____ R/7=2
3^3 ___ 27 _____ R/7=6
3^4 ___ 81 _____ R/7=4
3^5 ___ 243 _____ R/7=5
3^6 ___ 729 _____ R/7=1
3^7 ___ 2187 _____ R/7=3
3^8 ___ 6561 _____ R/7=2
3^9 ___ 19683 _____ R/7=6
3^10 ___ 59049 _____ R/7=4
3^11 ___ 177147 _____ R/7=5


the remainder pattern repeats every six powers


777777/6=129629 R3; so the remainder for (3^777777)/7 is 6