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Displaying similar documents to “Statistical methods in physico-chemical characterization of newly synthesized compounds.”

Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi

Jean-Marc Deshouillers, François Hennecart, Bernard Landreau (1998)

Acta Arithmetica

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Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture...