Question

Chứng minh rằng:

B = 5²⁰⁰⁸ + 5²⁰⁰⁷ + 5²⁰⁰⁶ chia hết cho 31

Answer 1

Ta có :

\(B=5^{2008}+5^{2007}+5^{2006}\)

\(\Rightarrow B=5^{2016}\left(5^2+5+1\right)\)

\(\Rightarrow B=5^{2016}.31\)

=> B chia hết cho 31