Question

Chứng minh rằng 7.5²ⁿ+12.6ⁿ chia hết cho 19

Answer 1

\(5^2=25=6\) [19]

\(\Rightarrow A=7.6^n+12.6^n=19.6^n\) [19]

Do đó: \(A⋮19\)

Answer 2

7.5²ⁿ + 12.6ⁿ

= 7.5²ⁿ + ( 19 - 7 ). 6ⁿ

= 7.5²ⁿ + 19. 6ⁿ - 7.6ⁿ

= 7.5²ⁿ - 7.6ⁿ + 19. 6ⁿ

= 7(5²ⁿ - 6ⁿ ) + 19.6ⁿ

= 7(25ⁿ - 6ⁿ ) + 19.6ⁿ

Xét 7(25ⁿ - 6ⁿ ) \(⋮\) 19; 19.6^{n \(⋮\)}19

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