Results 171 to 180 of about 1,000 (210)
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The Mathematical Gazette, 2012
Summary: Given that it took until the 19th century for the case \(n=5\) of Fermat's last theorem to be settled, it is not surprising that Fermat's claim of having a proof for all exponents greater than 2 is nowadays treated with considerable scepticism.
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Summary: Given that it took until the 19th century for the case \(n=5\) of Fermat's last theorem to be settled, it is not surprising that Fermat's claim of having a proof for all exponents greater than 2 is nowadays treated with considerable scepticism.
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2015
Euler, after a cursory reading of Wallis’s Opera Mathematica, mistakenly attributed the first serious study of nontrivial solutions to equations of the form \(x^{2} - Dy^{2} = 1\), where x ≠ 1 and y ≠ 0, to John Pell. However, there is no evidence that Pell, who taught at the University of Amsterdam, had ever considered solving such equations.
Titu Andreescu, Dorin Andrica
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Euler, after a cursory reading of Wallis’s Opera Mathematica, mistakenly attributed the first serious study of nontrivial solutions to equations of the form \(x^{2} - Dy^{2} = 1\), where x ≠ 1 and y ≠ 0, to John Pell. However, there is no evidence that Pell, who taught at the University of Amsterdam, had ever considered solving such equations.
Titu Andreescu, Dorin Andrica
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2014
In February, 1657, Fermat challenged the English mathematicians John Wallis (1616–1703) and Lord William V. Brouncker (1620–1684) to solve the non-linear diophantine equation \(x^{2} - dy^{2} = 1\), where d is nonsquare and positive. The amateur French mathematician Bernard de Bessey (ca. 1605–1675) solved it for d ≤ 150.
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In February, 1657, Fermat challenged the English mathematicians John Wallis (1616–1703) and Lord William V. Brouncker (1620–1684) to solve the non-linear diophantine equation \(x^{2} - dy^{2} = 1\), where d is nonsquare and positive. The amateur French mathematician Bernard de Bessey (ca. 1605–1675) solved it for d ≤ 150.
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2003
The so-called Pell equation x2 − ny2 = 1 (wrongly attributed to Pell by Euler) is one of the oldest equations in mathematics and it is fundamental to the study of quadratic Diophantine equations. The Greeks studied the special case x2 − 2y2 = 1 because they realized that its natural number solutions throw light on the nature of \(\sqrt{2}\). There is a
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The so-called Pell equation x2 − ny2 = 1 (wrongly attributed to Pell by Euler) is one of the oldest equations in mathematics and it is fundamental to the study of quadratic Diophantine equations. The Greeks studied the special case x2 − 2y2 = 1 because they realized that its natural number solutions throw light on the nature of \(\sqrt{2}\). There is a
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PELL’S EQUATIONS IN GAUSSIAN INTEGERS
JP Journal of Algebra, Number Theory and Applications, 2019Summary: From Hurwitz's approach of complex continued fractions, we build a complex theory of the Pell's equation. In this paper, we study the complex theory of the Pell's equation, \(x^2-Dy^2=2\), that is, finding its solutions in Gaussian integers, using Hurwitz complex continued fraction, hence, generalizing it to the Pell's equation \(x^2-Dy^2=2^n\)
Kharbuki, Algracia, Singh, Madan Mohan
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2002
Summary: Since the time of Archimedes, mathematicians have challenged their peers with a Diophantine equation that is satisfied by huge integers. The article discusses the algorithmic efficiency of various solution methods.
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Summary: Since the time of Archimedes, mathematicians have challenged their peers with a Diophantine equation that is satisfied by huge integers. The article discusses the algorithmic efficiency of various solution methods.
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The Set of Automorphisms of Pell Forms and Pell Equations
2022d = k(2) + 4 for some integer k >= 2. In this work, we first determined the set of automorphisms of the Pell form F-delta(x, y) = x(2) - dy(2) of discriminant delta = 4d. Later, we deduced the set of all integer solutions of the Pell equations F-delta(x, y) = +/- 1 and F-delta(x, y) = +/- k(2).
TEKCAN, AHMET, Biberoglu, Gulsah
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Journal of Mathematical Sciences, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Primality tests, linear recurrent sequences and the Pell equation
Ramanujan Journal, 2021Simone Dutto +2 more
exaly