What is a formula for all integers n for which a regular polygon with n sides can be constructed using a ruler and compass construction?
2026-03-25 22:01:46.1774476106
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Some help needed with a geometry question
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I typed the search terms "regular polygon compass ruler" at the On-Line Encyclopedia of Integer Sequences and got sequence A003401.
The Gauss-Wantzel theorem gives necessary and sufficient conditions for the constructibility of regular polygons: a regular $n$-gon can be constructed with compass and straightedge if and only if $n=2^kp_1p_2...p_t$ where $k$ and $t$ are non-negative integers, and each $p_i$ is a distinct Fermat prime. However, only five Fermat primes are currently known, and it is unknown whether any more even exist. This makes the answer to your question an open problem in mathematics.