wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Show that exactly one of the numbers n,n+2,n+4 is divisible by 3.

Open in App
Solution

Case I:
If n=3q
n+4=3q+4n+2=3q+2
here n is only divisible by 3
Case II:
If n=3q+1
n+4=3q+5n+2=3q+3=3(q+1)
Here only n+2 is divisible by 3
Case III:
If n=3q+2
n+2=3q+4
n+4=3q+2+4 =3q+6
Here only n+4 is divisible by 3
Hence, only one of the numbers n,n+2,n+4 is divisible by 3.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Why Divisibility Rules?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon