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math.NT2025
Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions
Yuhi Kamio
Paul Erdős posed a problem on the asymptotic estimation of decomposing 1 into a sum of infinitely many unit fractions in \cite{Erd80}. We point out that this problem can be solved…
math.NT2023
Quadratic residues and domino tilings
Yuhi Kamio, Junnosuke Koizumi, Toshihiko Nakazawa
The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection be…