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For any positive integer n, show that one and only one out of n, n+3, n+6, or n+9 is divisible by 4.

For any positive integer n, show that one and only one out of n, n+3, n+6, or n+9 is divisible by 4.

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear Palak
 
n can be of the form of 
i) 4n
ii) 4n + 1
iii) 4n + 2
iv) 4n + 3
 
Now using 1st case
4n, 4n+ 3, 4n + 6 , 4n + 9
Only 4n is divisible by 4
 
Now using 2nd case
4n + 1, 4n + 4, 4n + 7, 4n + 10
Only 4n + 4 = 4 (n+1) is divisible by 4
 
similarly you can do this for rest of the cases and find that only one number is divisible by 4
 
Regards
Arun (askIITians forum expert)

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