+) Chứng minh C⋮5
Có 5⋮5; \(\text{5}^{2}\)⋮5; \(\text{5}^{3}\)⋮5;...;\(\text{5}^{20}\)⋮5
⇒\(5+\text{5}^{2}+\text{5}^{3}+...+\text{5}^{20}\)⋮5
Vậy C⋮5
+) Chứng minh C⋮6
C=\(5+\text{5}^{2}+\text{5}^{3}+...+\text{5}^{20}\)
=\((5+\text{5}^{2}+\text{5}^{3}+\text{5}^{4})+...+(\text{5}^{17}+\text{5}^{18}+\text{5}^{19}+\text{5}^{20})\)
=\(5(1+\text{5}^{1}+\text{5}^{2}+\text{5}^{3})+...+\text{5}^{17}(1+\text{5}^{1}+\text{5}^{2}+\text{5}^{3})\)
=\((5+...+\text{5}^{17}).(1+\text{5}^{1}+\text{5}^{2}+\text{5}^{3})\)
=\((5+...+\text{5}^{17}).156\)
=\((5+...+\text{5}^{17}).26.6\)⋮\(6 \)
Vậy C⋮6