Completing an universal $m$ -gonal form with a closing unary piece

preprint2021arXivOpen access

In this paper, we show that for any $m$ -gonal form $F_m(\mathbf x)$ with $m \ge 12$ which represents every positive integer up to $m-4$ , by putting together only unary $m$ -gonal form, we may complete an universal form.

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Completing an universal $m$ -gonal form with a closing unary piece

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Completing an universal mmm-gonal form with a closing unary piece

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Completing an universal $m$ -gonal form with a closing unary piece