S gồm: (2017 - 0) : 1 + 1 = 2018 số
S = 1 + 5 + 5^2 + 5^3 + 5^4 +....+ 5^2017
    = (1+ 5) + (5^2 + 5^3) + ... + (5^2016 + 5^2017)
    = 6 + 5.(1 + 5) + 5^4.(1 + 5) + ... + 5^2016.(1 + 5)
    = 6 + 5.6 + 5^4.6 +...+ 5^2016.6
    = 6.(1 + 5 + 5^4 + ...+ 5^2016)
=> S chia hết cho 3

S=1+5+5^2+5^3+5^4+....+5^2017

= (1+5) + (5^2+5^3) + (5^4+5^5) + ... + (5^2016+5^2017)
= 6 + 5.(1+5) + 5^4.(1+5) + ... + 5^2016.(1+5)
= 6+5.6+5^4.6+...+5^2016.6
= (1+5+5^4+...+5^2016).6 chia hết cho 3 
từ đó suy ra  S chia hết cho 3