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arXiv · 1903.00169

On a problem of Perron

Michele Elia
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Abstract

It is shown that a partition $\mathfrak A\cup \mathfrak B$ of the set $\mathbb F_{p^m}^*=\mathbb F_{p^m}-\{0 \}$, with $|\mathfrak A|=|\mathfrak B|$, is the separation into squares and non squares, if and only if the elements of $\mathfrak A$ and $\mathfrak B$ satisfy certain additive properties, thus providing a purely additive characterization of the set of squares in $\mathbb F_{p^m}$.

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Michele Elia. 2019-03-01. On a problem of Perron. https://arxiv.org/abs/1903.00169

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