Question

Cho A = 51^n  +   47^102 ( n thuộc N )

Chứng minh rằng A chia hết cho 10

Answer 1

Ta có:

\(51^n\equiv1\left(mod10\right)\)

\(47^2\equiv-1\left(mod10\right)\)

\(\Rightarrow47^{102}\equiv-1\left(mod10\right)\)

\(\Rightarrow A=51^n+47^{102}\equiv1+\left(-1\right)\left(mod10\right)\)

\(\Rightarrow A=51^n+47^{102}⋮10\left(đpcm\right)\)

Answer 2

A = 51ⁿ + 47¹⁰²

A = (...1) + 47¹⁰⁰.47²

A = (...1) + (47⁴)²⁵.(...9)

A = (...1) + (...1)²⁵.9

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

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

\(A=\left(...0\right)⋮10\left(đpcm\right)\)