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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.
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Solution
We have:
\[P(n): n^3 + n\text{ is divisible by } 3 . \]
\[\text{ Thus, we have: } \]
\[P(3) = 3^3 + 3 = 27 + 3 = 30 \]
\[\text{ It is divisible by } 3 . \]
\[\text{ Hence, P(3) is true } . \]
\[\text{ Now } , \]
\[P(4) = 4^3 + 4 = 64 + 4 = 68 \]
\[\text{ It is not divisible by 3} . \]
\[\text{ Hence, P(4) is not true} .\]
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