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Found problems: 1

2022 3rd Memorial "Aleksandar Blazhevski-Cane", P5
We say that a positive integer $n$ is [i]memorable[/i] if it has a binary representation with strictly more $1$'s than $0$'s (for example $25$ is memorable because $25=(11001)_{2}$ has more $1$'s than $0$'s). Are there infinitely many memorable perfect squares? [i]Proposed by Nikola Velov[/i]
memorable binary perfect square algebra number theory perfect squares