mk làm câu A = ... nha
ta có A = 3 + 33 + 35 + ...+31991
A = ( 3 + 33 + 35 ) + ( 37 + 3 9 + 311 ) + ... + ( 31987 + 31989 + 1991 )
A = 3 . (1 + 3 + 32 ) + 37 . ( 1 + 3 + 32 ) + ... + 31987 . ( 1 + 3 + 32 )
A = 3 . 13 + 37 . 13 + ... + 31987. 13
A = 13 . ( 3 + 37 + ... + 31987 ) ( VÌ 13 CHIA HẾT CHO 13 )
=> A CHIA HẾT CHO 13
\(C=3+3^3+3^5+.....+3^{1991}.\)
\(=\left(3+3^3+3^5+3^7\right)+\left(3^9+3^{11}+3^{13}+3^{15}\right)+.....+\left(3^{1985}+3^{1987}+3^{1989}+3^{1991}\right)\)
\(=3.\left(1+3^2+3^4+3^6\right)+3^9\left(1+3^2+3^4+3^6\right)+....+3^{1985}\left(1+3^2+3^4+3^6\right)\)
\(=3.820+3^9.820+....+3^{1985}.820\)
\(=820\left(3+3^9+....+3^{1985}\right)\)
\(=41.20\left(3+3^9+...+3^{1985}\right)\)
\(\Rightarrow C⋮41\)
