Ta có: \(B=3+3^3+3^5+\cdots+3^{1991}\)
\(=\left(3+3^3\right)+\left(3^5+3^7\right)+\cdots+\left(3^{1989}+3^{1991}\right)\)
\(=3\left(1+3^2\right)+3^5\left(1+3^2\right)+\cdots+3^{1989}\left(1+3^2\right)\)
\(=\left(1+3^2\right)\left(3+3^5+\cdots+3^{1989}\right)\)
\(=10\left(3+3^5+\cdots+3^{1989}\right)\) ⋮10
Ta có: \(B=3+3^3+3^5+\cdots+3^{1991}\)
\(=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+\cdots+\left(3^{1987}+3^{1989}+3^{1991}\right)\)
\(=3\left(1+3^2+3^4\right)+3^7\left(1+3^2+3^4\right)+\cdots+3^{1987}\left(1+3^2+3^4\right)\)
\(=91\left(3+3^7+\ldots+3^{1987}\right)\) ⋮13
Ta có: \(B=3+3^3+3^5+\cdots+3^{1991}\)
\(=3+3^2\left(3+3^3+\cdots+3^{1989}\right)\)
\(=3+9\left(3+3^3+\cdots+3^{1989}\right)\)
=>B không chia hết cho 9
Ta có: \(B=3+3^3+3^5+\cdots+3^{1991}\)
\(=3+3^3\left(1+3^2+\cdots+3^{1988}\right)\)
\(=3+27\left(1+3^2+\cdots+3^{1988}\right)\)
=>B không chia hết cho 27
