\(A=3+3^3+3^5+3^7+...+3^{2015}⋮13and41\)
\(A=\left(3+3^2+3^5\right)+\left(3^7+3^9+3^{11}\right)+...+\left(3^{2011}+3^{2013}+3^{2015}\right)\)
\(A=3.\left(1+3^2+3^4\right)+3^7.\left(1+3^2+3^4\right)+...+3^{2011}.\left(1+3^2+3^4\right)\)
\(A=3.91+3^7.91+...+3^{2011}.91\)
\(A=3.7.13+3^7.7.13+...+3^{2011}.7.13\)
\(A=13.\left(3.7+3^7.7+...+3^{2011}.7\right)\)
\(forA=13.\left(3.7+3^7.7+...+3^{2011}.7\right)soA⋮13\)
\(A=\left(3+3^3+3^5+3^7\right)+...+\left(3^{2009}+3^{2011}+3^{2013}+3^{2015}\right)\)
\(A=3.\left(1+3^2+3^4+3^6\right)+...+3^{2009}\left(1+3^2+3^4+3^6\right)\)
\(A=3.820+...+3^{2009}.820\)
\(A=3.20.41+...+3^{2009}3.20.41\)
\(A=41.\left(3.20+...+3^{2009}.20\right)\)
\(forA=41.\left(3.20+...+3^{2009}.20\right)⋮41soA=3+3^3+3^5+3^7+...+3^{2015}⋮41\)
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