Relevant bibliographies by topics / Problem of Diophantus

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Problem of Diophantus'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Problem of Diophantus"

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Gyarmati, Katalin. "On a problem of Diophantus." Acta Arithmetica 97, no. 1 (2001): 53–65. http://dx.doi.org/10.4064/aa97-1-3.

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Dujella, Andrej. "Generalization of a problem of Diophantus." Acta Arithmetica 65, no. 1 (1993): 15–27. http://dx.doi.org/10.4064/aa-65-1-15-27.

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Dujella, Andrej, and Clemens Fuchs. "On a problem of Diophantus for rationals." Journal of Number Theory 132, no. 10 (October 2012): 2075–83. http://dx.doi.org/10.1016/j.jnt.2012.04.004.

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Harrington, Joshua, and Lenny Jones. "A modification of a problem of Diophantus." Mathematica Slovaca 68, no. 6 (December 19, 2018): 1343–52. http://dx.doi.org/10.1515/ms-2017-0185.

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Abstract An old question, due to Diophantus, asks to find sets of rational numbers such that 1 added to the product of any two elements from the set is a square. We are concerned here with a modification of this question. Let t ≥ 2 be an integer, and let 𝔽 be a field. For d ∈ 𝔽, define ft,d: 𝔽t → 𝔽 as $$\begin{array}{} \displaystyle f_{t,d}(x_1,x_2,\ldots,x_{t}):=x_1x_2\cdots x_{t}+d. \end{array}$$ For any nonempty subset S of 𝔽, we say $$\begin{array}{} \displaystyle S ~~\text{is}~~ {f_{t,d}-closed} ~~\text{if}~~ \left\{f_{t,d}(x_1,x_2,\ldots,x_{t}):x_i\in S\text{ and distinct}\right\}\subseteq S. \end{array}$$ For any integer n, with t≤ n≤ |𝔽|, let 𝒰(n,t,d) be the union of all ft,d-closed subsets S of 𝔽 with |S|=n. In this article, we investigate values of n,t,d for which 𝒰(n,t,d) = 𝔽, with particular focus on t = n – 1, where n ∈ {3,4}. Moreover, if 𝒰(n,t,d)≠ 𝔽, we determine in many cases the exact elements of the set 𝔽∖ 𝔽(n,t,d).
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Bugeaud, Yann, and Katalin Gyarmati. "On generalizations of a problem of Diophantus." Illinois Journal of Mathematics 48, no. 4 (October 2004): 1105–15. http://dx.doi.org/10.1215/ijm/1258138502.

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Dujella, Andrej, and Florian Luca. "On a Problem of Diophantus with Polynomials." Rocky Mountain Journal of Mathematics 37, no. 1 (February 2007): 131–57. http://dx.doi.org/10.1216/rmjm/1181069322.

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BUGEAUD, YANN, and ANDREJ DUJELLA. "On a problem of Diophantus for higher powers." Mathematical Proceedings of the Cambridge Philosophical Society 135, no. 1 (July 2003): 1–10. http://dx.doi.org/10.1017/s0305004102006588.

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DUJELLA, ANDREJ, and CLEMENS FUCHS. "COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER." Journal of the London Mathematical Society 71, no. 01 (February 2005): 33–52. http://dx.doi.org/10.1112/s002461070400609x.

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Dujella, Andrej, and Clemens Fuchs. "A Polynomial Variant of a Problem of Diophantus and Euler." Rocky Mountain Journal of Mathematics 33, no. 3 (September 2003): 797–811. http://dx.doi.org/10.1216/rmjm/1181069929.

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Dujella, Andrej, and Clemens Fuchs. "Complete solution of the polynomial version of a problem of Diophantus." Journal of Number Theory 106, no. 2 (June 2004): 326–44. http://dx.doi.org/10.1016/j.jnt.2003.12.011.

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Dissertations / Theses on the topic "Problem of Diophantus"

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Davis, Tinka. "Forty two problems of first degree from Diophantus’ Arithmetica." Thesis, Wichita State University, 2010. http://hdl.handle.net/10057/5437.

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This work brings to the audience Diophantus' problems of first degree in a literal word for word English translation from Ver Eecke's French translation of Arithmetica. In addition, these problems are accompanied by commentary in modern notation, as well as some modern and general solutions to appropriate problems.
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
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Nováková, Hana. "Analýza a priori jako součást přípravy učitele na výuku." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-328185.

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5 TITLE: A priori analysis as a part of teacher's lesson planning AUTHOR: Mgr. Hana Nováková DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. This thesis focuses on a priori analysis as a part of teacher's lesson planning. The theoretical background consists of the Theory of didactical situations in Mathematics (TDSM). In TDSM, the a priori analysis is seen as one of the teacher's tools that he/she has when planning a lesson. The goal of the thesis is to analyse differences between a priori analysis as described in TDSM and the reality in teacher's practice, to compare lesson plans of experienced teachers with those of students and demonstrate the significance and application of a priori analysis in teacher's and researcher's practice. The thesis consists of three parts, theoretical, experimental and applicational. In the theoretical part, the main concepts of TDSM linked with a priori analysis are explained and the issue of teacher's lesson planning is presented. The experimental part starts with a pre-experiment. Its results contributed to precise the structure of a priori analysis for further use. During the main experiment, the lesson plans of experienced teachers were compared with those of pre-service teachers. The differences and the...
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Book chapters on the topic "Problem of Diophantus"

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Long, Calvin, and Gerald Bergum. "On a Problem of Diophantus." In Applications of Fibonacci Numbers, 183–91. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-015-7801-1_17.

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Arkin, Joseph, and Gerald Bergum. "More on the Problem of Diophantus." In Applications of Fibonacci Numbers, 177–81. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-015-7801-1_16.

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Dujella, Andrej. "A Problem of Diophantus and Pell Numbers." In Applications of Fibonacci Numbers, 61–68. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5020-0_9.

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Dujella, Andrej. "On the Exceptional Set in the Problem of Diophantus and Davenport." In Applications of Fibonacci Numbers, 69–76. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5020-0_10.

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Meskens, Ad. "Coda: Hilbert’s tenth problem." In Travelling Mathematics - The Fate of Diophantos' Arithmetic, 171–72. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0643-1_9.

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Charbonneau, Louis, and Jacques Lefebvre. "Placement and Function of Problems in Algebraic Treatises from Diophantus to Viète." In Approaches to Algebra, 155–65. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-1732-3_12.

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Herrin, Judith. "Mathematical Mysteries in Byzantium." In Margins and Metropolis. Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691153018.003.0015.

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This chapter examines how the mathematical mysteries of Diophantus were preserved, embellished, developed, and enjoyed in Byzantium by many generations of amateur mathematicians like Pierre de Fermat, who formulated what became known as Fermat's last theorem. Fermat was a seventeenth-century scholar and an amateur mathematician who developed several original concepts in addition to the famous “last theorem.” One of his sources was the Arithmetika, a collection of number problems written by Diophantus, a mathematician who appears to have flurished in Alexandria in the third century AD. It was through the Greek text translated into Latin that Fermat became familiar with Diophantus's mathematical problems, and in particular the one at book II, 8, which encouraged the formulation of his own last theorem. Fermat's last theorem claims that “the equation xn + yn = zn has no nontrivial solutions when n is greater than 2”.
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Katz, Victor J., and Karen Hunger Parshall. "Later Alexandrian Developments." In Taming the Unknown. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691149059.003.0004.

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This chapter traces the development of mathematics in the vibrant research and cultural complex that began to coalesce around the Museum and Library in Alexandria around 300 BCE. This distinguished scholastic history lasted even during the Roman takeover of the city in 27 BCE, as scholars continued to gather and work at the Museum despite the unsettled social climate. Among them, Diophantus (fl. 250 CE) produced one of the first Greek texts that can be said to have both a heritage and a history that may be termed algebraic—namely, his compilation of problems entitled Arithmetica. Only ten books remain of the original thirteen Arithmetica, and the chapter provides a sampling of these.
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