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Question

7n3n is always divisible by


A

6

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B

10

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C

4

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D

8

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Solution

The correct option is C

4


Substituting n=1, we get
7131=4
Let P(n):7n3n is divisible by 4
P(1) is true
Assume P(k) is true
7k3k is divisible by 47k3k=4mNow, 7k+13k+1=7.(7k3k)+4.3k=4.(7m+3k)divisible by 4
P(k+1) is true

Hence, P(n) is true.


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