Gonitzoggoβ
This is a proof based problem added for learning purposes and does not accept submissions.
You can view the solution by clicking on the solution tab.
You can view the solution by clicking on the solution tab.
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Let $(a_k)_{1\leq k\leq 2023}$ be the required sequence.
\[a_k=3^{2024-k}\cdot 4^{k-1}\]
Here, the sum of the squares of two consecutive terms \[a_k^2+a_{k+1}^2=(3^{2024-k}\cdot 4^{k-1})^2+(3^{2023-k}\cdot 4^{k})^2=(3^{2023-k}\cdot 4^{k-1})^2(3^2+4^2)=(3^{2023-k}\cdot 4^{k-1}\cdot 5)^2\]
Which is a square.
So, such a sequence exists.