M. Nathanson

activity

20002026

most citedUnique representation bases for the integers

34 citations · 268 across the 120 of their papers we have counts for

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Showing 2021 · math.NTShow all

4 papers · 2 filters

math.NT2021

Generalizations of Menon's arithmetic identity

Melvyn B. Nathanson

Menon's identity is $\sum_{a \in A}^{m} (a - 1, m) = d (m) φ (m)$ , where $A$ is a reduced set of residues modulo $m$ . This paper contains elementary proofs of some generalizations of this…

math.NT2021★ 4 cited

The Bose-Chowla argument for Sidon sets

Melvyn B. Nathanson

Let $h \geq 2$ and let $A = (A_{1}, \dots, A_{h})$ be an $h$ -tuple of sets of integers. For nonzero integers $c_{1}, \dots, c_{h}$ , consider the linear form $φ= c_1 x_1 + c_2x_…

math.NT2021

An inverse problem for finite Sidon sets

Melvyn B. Nathanson

Here is a direct problem for Sidon sets: Given a linear form $φ = c_{1} x_{1} + \dots + c_{h} x_{h}$ , construct and describe sets $A$ that are Sidon sets for $φ$ . This paper considers an…

math.NT2021★ 4 cited

Sidon sets for linear forms

Melvyn B. Nathanson

Let $φ (x_{1}, \dots, x_{h}) = c_{1} x_{1} + \dots + c_{h} x_{h}$ be a linear form with coefficients in a field $F$ , and let $V$ be a vector space over $F$ . A nonempty subse…