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Found problems: 1

2025 India National Olympiad, P1
Consider the sequence defined by \(a_1 = 2\), \(a_2 = 3\), and \[ a_{2k+1} = 2 + 2a_k, \quad a_{2k+2} = 2 + a_k + a_{k+1}, \] for all integers \(k \geq 1\). Determine all positive integers \(n\) such that \[ \frac{a_n}{n} \] is an integer. Proposed by Niranjan Balachandran, SS Krishnan, and Prithwijit De.
induct divisibility recurrence infinite descent mathematical induction modular arithmetic number theory recurrence relations sequences