Question

Chứng minh rằng với mọi số n nguyên dương thì:

a/ (6²ⁿ + 19ⁿ - 2ⁿ⁺¹) chia hết cho 17

b/ (7.5²ⁿ + 12.6ⁿ) chia hết cho 19

c/ (5ⁿ⁺² + 26.5ⁿ + 8²ⁿ⁺¹) chia hết cho 59

Answer 1

bnag a,b,c luon

Answer 2

KNLNLKLFNK;KLNKALSKNK

Answer 3

\(5^{n+2}+26.5^n+8^{2n+1}\)

\(=5^n.5^2+26.5^n+8^{2n}.8\)

\(=5^n.25+26.5^n+64^n.8\)

\(=5^n.25+34.5^n-8.5^n+64^n.8\)

\(=5^n\left(25+34\right)+8\left(64^n-5^n\right)\)

\(=5^n.59+8\left(64^n-5^n\right)\)

Áp dụng t/c: Nếu \(\left(a-b\right)⋮m\)thì \(\left(a^n-n^n\right)⋮m\)

\(\Rightarrow8\left(64^n-5^n\right)⋮59\)

Mà \(5^n.59⋮59\)nên \(5^{n+2}+26.5^n+8^{2n+1}⋮59\left(đpcm\right)\)