Question

[Phan Hải Đăng]

1, Cho \(a_1,a_2,a_3,...,a_{2016}\)là các STN chia hết cho 3

CMR \(A=a_1^3+a_2^3+...+a_{2016}^3\)chia hất cho 3

Answer 1

[ʚ๖ۣۜKɦáηɦ ๖ۣۜHυүềηɞ‏]

\(a_1,a_2,a_3,...,a_{2016}⋮3\)

nên \(a_1=3k_1;a_2=3k_2;a_3=3k_3;...;a_{2016}=3k_{2016}\)

\(\Rightarrow a_1^3=27k_1^3⋮3\)

\(a_2^3=27k_2^3⋮3\)

\(a_3^3=27k_3^3⋮3\)

...

\(a_{2016}^3=27k_{2016}^3⋮3\)

\(\Rightarrow A⋮3\)(đpcm)