If P (n) is the statement “n3 + n is divisible by 3”,
Question:

If P (n) is the statement “n3 + n is divisible by 3″, prove that P (3) is true but P (4) is not true.

Solution:

We have:

$P(n): n^{3}+n$ is divisible by 3 .

 

Thus, we have :

$P(3)=3^{3}+3=27+3=30$

It is divisible by $3 .$

 

Hence, $P(3)$ is true.

Now,

$P(4)=4^{3}+4=64+4=68$

It is not divisible by 3 .

 

Hence, $P(4)$ is not true.

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