Prime-universal diagonal quadratic forms
Abstract
A (positive definite and integral) quadratic form is said to be prime-universal if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all prime-universal diagonal quaternary quadratic forms under two conjectures proposed by themselves. In this article, we classify all prime-universal diagonal quadratic forms regardless of ranks. Furthermore, we prove, so called, 67-Theorem for a diagonal quadratic form to be prime-universal.
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