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Belarusian Mathematical Olympiad

Algebra Difficulty 5.1 AIME, harder Prove it Belarus

Define the sequence $a_0, a_1, a_2, \dots$ by $a_n = 2^n + 2^{\lfloor n/2 \rfloor}$ . Prove that there are infinitely many terms of the sequence which can be expressed as a sum of (two or more) distinct terms of the sequence, as well as infinitely many of those which cannot be expressed in such a way.

Solution

2. See IMO - 2018 Shortlist, Problem N3.

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