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Definability of arithmetical operations from binary quadratic forms
, 1998 Ivan Korec
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High-Pressure Phase Behavior of α-Olefin + <i>n</i>-Hexane + Ethylene/1-Octene Copolymer Systems: Experimental Study and Modeling. [PDF]
Polymers (Basel)Zhang R +5 more
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On Some Congruence Conjectures Involving Binary Quadratic Forms
Guo-Shuai Mao
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Whether groups value agreement or dissent depends on the strength of consensus. [PDF]
PLoS OneMellody JC.
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Percolation with Distance-Dependent Site Occupational Probabilities. [PDF]
Entropy (Basel)Lambrou E, Argyrakis P.
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A robust color image encryption algorithm based on 2D-SQSM hyperchaotic map and cyclic shift scrambling. [PDF]
PLoS OneLiu F, Wu S.
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Supercongruences and binary quadratic forms
Acta Arithmetica, 2021Summary: Let \(p > 3\) be a prime, and let \(a,b\) be two rational \(p\)-adic integers. We present general congruences for \(\sum_{k=0}^{p-1}\binom{a}{k}\binom{-1-a}{k}\frac{p}{k+b}\pmod{p^2} \). Let \(\{D_n\}\) be the Domb numbers given by \(D_n=\sum_{k=0}^n\binom{n}{k}^2\binom{2k}{k}\binom{2n-2k}{n-k} \).
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Diagonal quadratic forms representing all binary diagonal quadratic forms
The Ramanujan Journal, 2017For a positive integer \(n\), a positive definite integral quadratic form is \(n\)-universal if it represents all positive definite integral quadratic forms of rank \(n\). For example, the quinary quadratic form \(x_1^2+x_2^2+x_3^2+x_4^2+ x_5^2\) is \(2\)-universal, by a classical result of \textit{L. J. Mordell} [Q. J. Math., Oxf. Ser.
Ji, Yun-Seong +2 more
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