Ta có : S = 5+5^2+5^3+5^4+...+5^66
S =( 5+5^2+5^3) +( 5^4+5^5 + 5^6 ) + ...+(5^64+5^65+5^66)
S= 5. ( 1 + 5 + 5^2 ) + 5^4 . ( 1 + 5 + 5^2 ) + ..... + 5 ^64 . ( 1 + 5 + 5^2 )
S = 5.31 + 5^4 . 31 + ........... + 5^64 . 31
S = 31 . ( 5 + 5^4 + .... + 5^64 ) chia hết cho 31