5⁵-5⁴+5³=5³.(5²-5¹+5⁰)=5³.(25-5+1)=5³.21=5³.3.7 chia hết cho 7

=>ĐPCM

7⁶+7⁵-7⁴=7⁴.(7²+7¹-7⁰)=7⁴.(49+7-1)=7⁴.55=7⁴.5.11 chia hết cho 11

=>ĐPCM

\(3.\overline{abcabc}-605=3.\left(1000\overline{abc}+\overline{abc}\right)-605=3.1001.\overline{abc}-695=11\left(273\overline{abc}-55\right)⋮11\)

1) 5⁵ - 5⁴ + 5³ = 5³ . 5² - 5³ . 5 - 5³

= 5³ . ( 5² - 5 + 1 )

= 5³ . ( 25 - 5 - 1 )

= 5³ . 21

= 5³ . 3 . 7 chia hết cho 7

Vậy chứng minh 5⁵ - 5⁴ + 5³ chia hết cho7

2) 7⁶ + 7⁵ - 7⁴ = 7⁴ . 7² + 7⁴ . 7 - 7⁴

= 7⁴ . ( 7² + 7 - 1 )

= 7⁴ . ( 49 + 7 - 1 )

= 7⁴ . 55

= 7⁴ . 5 .11 chia hết cho 11

Vậy chứng minh 7⁶ + 7⁵ - 7⁴ chia hết cho 11

Tích mình nha !!!!!!!!!!!!!!!!!

o biết
 

\(\overline{3ab3}-\overline{3ba3}=3003-3003+\overline{ab0}-\overline{ba0}=10\left(\overline{ab}-\overline{ba}\right)=10\left(10a+b-10b-a\right)\)

\(=10\left(9a-9b\right)=90\left(a-b\right)⋮90\)

\(\overline{aaa}+\overline{bbb}=111.a+111.b=111\left(a+b\right)=37\times3\times\left(a+b\right)⋮37\)

\(\overline{abc}+\overline{bca}+\overline{cab}=\left(100a+10b+c\right)+\left(100b+10c+a\right)+\left(100c+10a+b\right)\)

\(=111\left(a+b+c\right)=37\times3\times\left(a+b+c\right)⋮37\)