Toán Lớp 6: (7^6 + 7^5 – 7^4) chứng minh chia hết cho 77

Question

Toán Lớp 6:  (7^6 + 7^5 – 7^4) chứng minh chia hết cho 77

huongtructram · Answer

Ta c&oacute;: (7^6+7^5-7^4)    =7^4.(7^2+7^1-1)   =7^4.(49+7-1)   =7^3.7.55=7^3.7.11   =7^3.(7.11)=7^3.77    V&igrave; 77⁝77&rArr; 7^3.77⁝77   &rArr;(7^6+7^5-7^4)⁝77   Vậy (7^6+7^5-7^4)⁝77

catlantuong · Answer

Giải      (7^6 + 7^5 &ndash; 7^4) chứng minh chia hết cho 77     Ta c&oacute;:     7^6 + 7^5 - 7^4     = 7 . 7^5 + 7 . 7^4 - 7 . 7^3     = 7 . (7^5 + 7^4 - 7^3)     V&igrave; 7  vdots 7 => 7 . (7^5 + 7^4 - 7^3)  vdots 7                          => 7^6 + 7^5 - 7^4  vdots 7     Lại c&oacute;:     7^6 + 7^5 - 7^4     = 7^4 . 7^2 + 7^4 . 7 - 7^4 . 1     = 7^4 . (7^2 + 7 - 1)     = 7^4 . (49 + 7 - 1)     = 7^4 . 55     = 7^4 . 5 . 11     V&igrave; 11  vdots 11 => 7^4 . 5 . 11  vdots 11                              => 7^6 + 7^5 - 7^4  vdots 11     M&agrave; (7;11) = 1     => 7^6 + 7^5 - 7^4  vdots 77     Vậy 7^6 + 7^5 - 7^4  vdots 77