IMO Shortlist 1969 problem 61

$(SWE 4)$ Let $a_0, a_1, a_2, \cdots$ be determined with $a_0 = 0, a_{n+1} = 2a_n + 2^n$ . Prove that if $n$ is power of $2$ , then so is $a_n$

Izvor: Međunarodna matematička olimpijada, shortlist 1969

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