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

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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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