Question

chứng minh rằng A= (\(^{5^5}\)-\(^{5^4}\)+\(5^3\)) chia hết cho 7

Answer 1

\(A=5^5-5^4+5^3\)

\(\Rightarrow A=5^3\left(5^2-5^1+1\right)\)

\(\Rightarrow A=5^3\left(25-5+1\right)\)

\(\Rightarrow A=5^3.21=5^3.3.7⋮7\)

\(\Rightarrow dpcm\)