5+5^2+5^3+...+5^2006=(5+5^4)+(5^2+5^5)+(5^3+5^6)+...+(5^2003+5^2006). =5.(1+5^3)+5^2.(1+5^3)+5^3.(1+5^3)+...+5^2003.(1+5^3).
= 5.126+5^2.126+5^3.125+...+5^2003.126
=126.(5+5^2+5^3+...+5^2003)chia hết cho 126. Vậy 5+5^2+5^3+...+5^2006 chia hết cho 126