I've seen formulas to verify if a number is a triangular number, a pentagonal number, or a hexagonal number, but I haven't seen a general formula for verifying if a number is an n-sided polygonal number. Does such a formula exist?
2026-03-29 15:44:18.1774799058
Is there an efficient, general formula to verify if a number is a n-sided polygonal number?
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Yes. The polygon number formula for the $n$th $r$-gonal number is $$\frac{n((r-2)n-(r-4))}{2}$$
Wolfram Mathworld has an article about it here.