Prove-that-p-is-a-prime-number-if-and-only-if-every-equiangular-polygon-with-p-sides-of-rational-lengths-is-regular-

Question Number 16641 by Tinkutara last updated on 24/Jun/17

$$\mathrm{Prove}\:\mathrm{that}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{if}\:\mathrm{and} \\ $$$$\mathrm{only}\:\mathrm{if}\:\mathrm{every}\:\mathrm{equiangular}\:\mathrm{polygon}\:\mathrm{with} \\ $$$${p}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{lengths}\:\mathrm{is}\:\mathrm{regular}. \\ $$

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