CMR NẾU ABCD 29THÌ A+3B+9C+27D CHIA HẾT CHO 29 HD

Bài 48: CMR nếu

abcd

29

thì a+3b+9c+27d chia hết cho 29

HD:

Ta có:

abcd

29

=

1000

a

+

100

b

+

10

c

+

d

29

( ) ( ) ( ) ( )

= + + + = − + − + − + −200a 200b 20c 2 29d 2001a 1 203b 3b 29c 9c 29d 2d 29

(

^{2001a 203b 29c 29d}

) (

^{a 3b 9c 27d}

)

²⁹= + + + − + + +

(

^{69.29a 7.29b 29c 29d}

) (

^{a 3b 9c 27d}

)

²⁹

Khi đó:

a

+ + +

3

b

9

c

27

d

29