Question

Bài 1 : cm 3²⁰¹⁰ + 5²⁰¹⁰ chia hết cho 13

bài 2: cm 24¹⁹¹⁷+ 14¹⁹¹⁷ chia hết cho 19

bài 3: cm vs n thuộc N*, ta có :

       a, 6²ⁿ+ 19ⁿ - 2ⁿ⁺¹ chia hết cho 17

       b, 6²ⁿ + 1 + 5ⁿ⁺² chia hết cho 31

      c, 21²ⁿ⁺¹+ 17²ⁿ⁺¹ + 15 chia hết cho 19

Answer 1

Bài 1:

 ta có 3^3 = 27 chia 13 dư 1

=> (3^3)^670 = 3^ 2010 chia 13 dư 1 (1) 
5^2 = 25 chia 13 dư (-1)

=> (5^2)^1005 chia 13 dư (-1)^ 1005 = (-1) (2) 
Từ (1); (2)

=> 3^2010+5^2010 chia 13 dư 1 + (-1) = 0 
hay 3^2010+5^2010 chia hết cho 13. 

Answer 2

bài 1:

32010=(33)670≡1670(mod13)" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvea,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">32010=(33)670≡1670(mod13)
52010=(52)1005≡(−1)1005(mod13)" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-table; float:none; font-family:helvea,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">52010=(52)1005≡(−1)1005(mod13)
32010+52010" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvea,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">32010+52010 chia hết cho 13

Answer 3

32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">32010+52010=(33)670+(52)1005=27670+251005=(26+1)670+(26−1)1005=26A+1670−11005=26A⋮13" role="presentation" style="border:0px; direction:ltr; display:table-cell !important; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:44.919em; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:center; white-space:nowrap; width:10000em; word-spacing:normal" class="MathJax_CHTML mjx-chtml mjx-full-width">=26A⋮13

Answer 4

giải hộ mik bài 2 và 3 vs