Question

chứng minh với mọi n : 6²ⁿ + 19ⁿ - 2ⁿ⁺¹ ​  chia hết cho 17

Answer 1

`[16]`

`= 36^n + 19^n - 2^n . 2`

`= 36^n - 2^n + 19^n - 2^n`

Áp dụng `a^n - b^n vdots a - b forall x in RR`.

`-> 36^n - 2^n vdots 34 vdots 17`

`-> 19^n - 2^n vdots 17`.

`-> (36^n - 2^n) + (19^n - 2^n) vdots 17 ( a, b vdots n -> a +-b vdots n)`.

Answer 2

Có: \(6^{2n}+19^n-2^{n+1}\)

\(=36^n+19^n-2^n.2\)

\(=\left(36^n-2^n\right)+\left(19^n-2^n\right)\)

\(=34^n+17^n⋮17\left(đpcm\right)\)