Question

chứng minh

51ⁿ+47¹⁰² chia hết cho 10

 

 

Answer 1

Ta có:

51ⁿ + 47¹⁰²

= (...1) + 47¹⁰⁰ . 47²

= (...1) + (47⁴)²⁵ . (...9)

= (...1) + (...1)²⁵ . (...9)

= (...1) + (...1) . (...9)

= (...1) + (...9)

= (...0) chia hết cho 10

=> đocm

Answer 2

\(^{51^n}\)luôn luôn có tận cùng bằng 1 (\(51^n\)=....1)
\(47^{102}\)=\(\left(47^4\right)^{25}\cdot47^2\)=......1 *....9=....9
=> \(51^n+47^{102}=.....1+.....9=.....0\)chia hết cho 10