Infinitely Many Multiples of Seven

Problem

A sequence $\{a_n\}$ satisfies $a_1 = 1$ and

a_n = a_{n-1} + a_{\lfloor n/2 \rfloor} \qquad (n \ge 2).

Prove that infinitely many terms of $\{a_n\}$ are divisible by $7$ .

Answer

Solution

Difficulty	8/10
Topics	number theory, sequences

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