Introduction to Mathematical Thinking-Problem 3

3.Say whether the following is true or false and support your answer by a proof.
For any integer $n$, the number $n^2+n+1$ is odd.

Proof: $n^2+n+1=n(n+1)+1$. As $n$ and $n+1$ are two consecutive integers, one of them must be even, so their product is even. Therefore, $n^2+n+1=n(n+1)+1$ is odd.

来源：CSDN

作者：yuh_yeet

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