Positive solutions of the diophantine equation by W. R. Utz

Subjects: “…Diophantine equation…”
Get full text

Lagrange, central norms, and quadratic Diophantine equations by R. A. Mollin

“…We consider the Diophantine equation of the form x2−Dy2=c, where c=±1,±2, and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. …”
Get full text

The Exponential Diophantine Equation 2x+by=cz by Yahui Yu, Xiaoxue Li

Get full text

The Diophantine equation x2+2k=yn, II by J. H. E. Cohn

Subjects: “…Diophantine equation.…”
Get full text

The diophantine equation x2+3m=yn by S. Akhtar Arif, Fadwa S. Abu Muriefah

Get full text

The Diophantine Equation 8x+py=z2 by Lan Qi, Xiaoxue Li

“…Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod  8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod  8), then the equation has only the solutions (p,x,y,z)=(2q-1,(1/3)(q+2),2,2q+1), where q is an odd prime with q≡1(mod  3); (iii) if p≡1(mod  8) and p≠17, then the equation has at most two positive integer solutions (x,y,z).…”
Get full text

Diophantine Equation Generated by the Subfield of a Circular Field by I. G. Galyautdinov, E. E. Lavrentyeva

Subjects: Get full text

On the Diophantine equation x2+2k=yn by S. Akhtar Arif, Fadwa S. Abu Muriefah

Get full text

On the Diophantine equation x3=dy2±q6 by Fadwa S. Abu Muriefah

Get full text

On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz by Yuanyuan Deng, Wenpeng Zhang

Get full text

The diophantine equation r2+r(x+y)=kxy by W. R. Utz

Subjects: “…Diophantine equations…”
Get full text

An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory by K. M. Abirami, Narayanan Veena, R. Srikanth, P. Dhanasekaran

“…An interdisciplinary approach of fuzzy theory with number theory, especially Diophantine equations, needs to be accomplished to overcome this problem. …”
Get full text

On the Diophantine equation x2+p2k+1=4yn by S. Akhtar Arif, Amal S. Al-Ali

Get full text

On the computation of the class numbers of some cubic fields by Manny Scarowsky, Abraham Boyarsky

Subjects: Get full text

On the System of Diophantine Equations x2-6y2=-5 and x=az2-b by Silan Zhang, Jianhua Chen, Hao Hu

“…Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x,y,z) of the system of Diophantine equations x2-6y2=-5 and x=2z2-1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x2-6y2=-5 and x=az2-b for each pair of integral parameters a,b. …”
Get full text

On Euler’s lemma by Juozas Juvencijus Mačys

Subjects: Get full text

Corrigendum to “On Parametric and Matrix Solutions to the Diophantine Equation x2 + dy2 − z2 = 0 Where d Is a Positive Square-Free Integer” by James D. Shaw, James Guyker

Get full text

RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem by Andrea Ossicini

“…Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fermat’s extraordinary equation. …”
Get full text

Efficient digital quadratic unconstrained binary optimization solvers for SAT problems by Robert Simon Fong, Yanming Song, Alexander Yosifov

“…To utilize them, we implement a 2-step [3-SAT]-[Max 2-SAT]-[QUBO] conversion procedure and present a novel approach using linear systems and Diophantine equation to calculate the number of both satisfied and violated clauses of the original 3-SAT instance from the transformed Max 2-SAT formulation. …”
Get full text

BPS states, conserved charges and centres of symmetric group algebras by Garreth Kemp, Sanjaye Ramgoolam

“…A characterization of Young diagrams in terms of content distribution functions relates these number sequences to diophantine equations. These content distribution functions can be visualized as connected, segmented, open strings in content space.…”
Get full text