Inspired by Dickson’s classification of regular diagonal ternary quadratic forms, we prove that there are no primitive regular ternary m-gonal forms when m is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next such prime by a product of the previous primes, a question of independent interest.

中文翻译：

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正则三元多边形形式

受Dickson对正对角三元二次形式的分类的启发，我们证明当m足够大时，没有原始正则三元m-多边形形式。为了做到这一点，我们构造了在某个二次域中是惰性的素数序列，并证明它们满足一定的不等式，该不等式以下一个素数的乘积（下一个独立利息问题）为下一个素数的边界。