## Exam-Style Question on Proof## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 401. This question is similar to one that appeared on an IB AA Standard paper (specimen) for 2021. The use of a calculator is allowed.

Consider the sum of the squares of any two consecutive odd integers.

(a) Show that \((2n + 1)^2 + (2n + 3)^2 = 8n^2 +16n + 10\) , where \(n \in \mathbb{Z} \)

(b) Hence, or otherwise, prove that the sum of the squares of any two consecutive odd integers is even.

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