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The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2005, Volume 35, Issue 2, pp. 547 - 571
We show that solving of the two-parametric family of quartic Thue equations x⁴ – 2mnx³y + 2 (m² – n² + 1 ) x² y² + 2mnxy³ + y⁴ = 1, using the method of... 
Integers | Mathematical theorems | Algebra | Diophantine equation | Logarithms | Trivial solutions | Number theory | Equations | Nontrivial solutions | Linear forms in logarithms | Thue equations | Simultaneous Pellian equations | FORMS | MATHEMATICS | NUMBER | DIOPHANTINE EQUATIONS | INEQUALITIES | THEOREM | linear forms in logarithms | simultaneous Pellian equations | 11D59 | 11J86 | 11D25 | 11B37
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2018, Volume 370, Issue 6, pp. 3803 - 3831
A set of positive integers is called a Diophantine tuple if the product of any two elements in the set increased by the unity is a perfect square. A conjecture... 
Simultaneous rational approximation of irrationals | Diophantine tuples | Linear forms in logarithms | System of Pellian equations | system of Pellian equations | NUMBER | LOGARITHMS | linear forms in logarithms | simultaneous rational approximation of irrationals | K-1 | FAMILY | K+1 | MATHEMATICS | M-TUPLES | TRIPLES | QUINTUPLES II | SIMULTANEOUS PELL EQUATIONS
Journal Article
ACTA MATHEMATICA HUNGARICA, ISSN 0236-5294, 10/2019, Volume 159, Issue 1, pp. 89 - 108
We study the extendibility of a D(-1)-pair {1, p}, where p is a Fermat prime, to a D(-1)-quadruple in Z[-t], t > 0. 
MATHEMATICS | FORM | Diophantine quadruple | D(-1)-TRIPLES | RING | linear form in logarithm | quadratic field | simultaneous Pellian equation
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 10/2019, Volume 159, Issue 1, pp. 89 - 108
We study the extendibility of a $$D(-1)$$ D ( - 1 ) -pair {1, p}, where p is a Fermat prime, to a $$D(-1)$$ D ( - 1 ) -quadruple in $$\mathbb{Z} [\sqrt{-t}], t... 
11J86 | 11D09 | Diophantine quadruple | Mathematics, general | Mathematics | linear form in logarithm | 11R11 | quadratic field | simultaneous Pellian equation
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 07/2016, Volume 39, Issue 3, pp. 1201 - 1224
In this paper, we study D(-1)-triples of the form {1, b, c} in the ring Z [root-t], t > 0, for positive integer b such that b is a prime, twice prime, and... 
Diophantine quadruples | Quadratic field | Linear form in logarithms | Simultaneous Pellian equations | MATHEMATICS | EXTENSIBILITY
Journal Article
Glasnik Matematicki, ISSN 0017-095X, 06/2015, Volume 50, Issue 1, pp. 43 - 63
In this paper we give some results about primitive integral elements α in the family of bicyclic biquadratic fields Lc= Q ( ((c-2) c)1/2, ((c+4) c)1/2) which... 
Totally real bicyclic biquadratic fields | Index form equations | Minimal index | P-adic case | Simultaneous Pellian equations | simultaneous Pellian equations | minimal index | p-adic case | totally real bicyclic biquadratic fields
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2016, Volume 39, Issue 3, pp. 1201 - 1224
In this paper, we study $$D(-1)$$ D ( - 1 ) -triples of the form $$\{1,b,c\}$$ { 1 , b , c } in the ring $${\mathbb {Z}}[\sqrt{-t}]$$ Z [ - t ] , $$t>0$$ t > 0... 
11J86 | 11D09 | Linear form in logarithms | Simultaneous Pellian equations | Mathematics, general | Mathematics | Applications of Mathematics | 11R11 | Diophantine quadruples | Quadratic field
Journal Article
GLASNIK MATEMATICKI, ISSN 0017-095X, 2015, Volume 50, Issue 1, pp. 43 - 63
In this paper we give some results about primitive integral elements alpha in the family of bicyclic biquadratic fields L-c = Q root(c - 2)c, root(c + 4)c)... 
MATHEMATICS | MATHEMATICS, APPLIED | minimal index | totally real bicyclic biquadratic fields | EQUATIONS | simultaneous Pellian equations | p-adic case | index form equations
Journal Article
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, ISSN 0081-6906, 09/2013, Volume 50, Issue 3, pp. 296 - 330
Let b = 2, 5, 10 or 17 and t > 0. We study the existence of D(-1)-quadruples of the form {1, b, c, d} in the ring Z[root-t]. We prove that if {1, b, c} is a... 
MATHEMATICS | NUMBER | PELL EQUATIONS | D(-1)-QUADRUPLES | simultaneous Pellian equations | Diophantine quadruples | quadratic field | linear form in logarithms
Journal Article
Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 2013, Volume 50, Issue 3, pp. 296 - 330
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2011, Volume 34, Issue 2, pp. 215 - 230
In this paper we prove that the only primitive solution of the Time inequality vertical bar x(4) - 2cx(3)y + 2x(2)y(2) + 2cxy(3) + y(4)vertical bar <= 6c + 4,... 
Simultaneous pellian equations | Thue equations | Continued fractions | FORMS | MATHEMATICS | continued fractions | DIOPHANTINE EQUATIONS | simultaneous pellian equations
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 2/2014, Volume 142, Issue 1, pp. 231 - 243
We study solutions of the Markoff–Rosenberger equation ax 2+by 2+cz 2=dxyz whose coordinates belong to the ring of integers of a number field and form a... 
geometric progression | 14G05 | Markoff equation | Mathematics, general | Mathematics | 11D45 | 11D25 | MATHEMATICS | ELLIPTIC-CURVES | ALGEBRAIC-CURVES | NORM FORM EQUATIONS | ZERO DIOPHANTINE EQUATIONS | SIMULTANEOUS ARITHMETIC PROGRESSIONS | PELLIAN EQUATIONS | INTEGRAL POINTS
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2011, Volume 41, Issue 4, pp. 1173 - 1182
Journal Article
Mathematical Communications, ISSN 1331-0623, 12/2009, Volume 14, Issue 2, pp. 341 - 363
In this paper we find a minimal index and determine all integral elements with the minimal index in two families of totally real bicyclic biquadratic fields... 
Totally real bicyclic biquadratic fields | Index form equations | Simultaneous pellian equations | Minimal index | MATHEMATICS | MATHEMATICS, APPLIED | minimal index | INTEGERS | totally real bicyclic biquadratic fields | RESOLUTION | QUARTIC NUMBER-FIELDS | simultaneous Pellian equations | SIMULTANEOUS PELL EQUATIONS | index form equations
Journal Article
Bulletin of the Belgian Mathematical Society - Simon Stevin, ISSN 1370-1444, 07/2005, Volume 12, Issue 3, pp. 401 - 412
It is proved that if k and d are positive integers such that the product of any two distinct elements of the set {F-2k, 5F(2k), 4F(2k+2), d} increased by 4 is... 
Fibonacci numbers | Diophantine m-tuple | Simultaneous Pellian equations | MATHEMATICS | diophantine m-tuple | PELL EQUATIONS | SIZE | DIOPHANTINE M-TUPLES | simultaneous Pellian equations | 11B39 | 11D09 | 11J68
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 6/2009, Volume 58, Issue 2, pp. 155 - 180
Journal Article
Journal of Number Theory, ISSN 0022-314X, 07/2001, Volume 89, Issue 1, pp. 126 - 150
A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct elements increased by 1 is a perfect square. We prove that... 
common terms in recurrence sequences | simultaneous Pellian equations | Diophantine m-tuples | linear form in logarithms | Common terms in recurrence sequences | Linear form in logarithms | Simultaneous Pellian equations | MATHEMATICS | NUMBER | SIMULTANEOUS PELL EQUATIONS
Journal Article
Glasnik Matematicki, ISSN 0017-095X, 06/2006, Volume 41, Issue 1, pp. 9 - 30
Journal Article
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