I would be happy if you let me know how to tackle this problem. Thanks.
2026-03-26 16:05:35.1774541135
Prove that every terms of a sequence defined by a recurrence relation is a perfect square.
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Hint: You're on the right track. There does exist a linear recurrence relation for a sequence defined by some square roots of $a_n$, but not necessarily the positive ones (e.g. instead of $b_6=5$, you might have $b_6=-5$). Can you try to find a recurrence relation from there?