\(S=\left(1+5+5^2\right)+\left(5^3+5^4+5^5\right)+...+\left(5^{64}+5^{65}+5^{66}\right)\\ S=\left(1+5+5^2\right)+5^3\left(1+5+5^2\right)+...+5^{64}\left(1+5+5^2\right)\\ S=\left(1+5+5^2\right)\left(1+5^3+...+5^{64}\right)\\ S=31\left(1+5^3+...+5^{64}\right)⋮31\)
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