Relevant bibliographies by topics / Problems of Diophantus' "Arithmetica"

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Problems of Diophantus' "Arithmetica"'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Problems of Diophantus' "Arithmetica""

1

Shiu, Peter. "The gaps between sums of two squares." Mathematical Gazette 97, no. 539 (2013): 256–62. http://dx.doi.org/10.1017/s0025557200005842.

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Problems concerning the setof numbers which are representable as sums of two squares have a long history. There are statements concerning W in the Arithmetic of Diophantus, who seemed to be aware of the famous identitywhich shows that the set W is ‘multiplicatively closed’. Since a square must be congruent to 0 or 1 (mod 4), it follows that members of W cannot be congruent to 3 (mod 4). Also, it is not difficult to show that a number of the form 4k + 3 must have a prime divisor of the same form dividing it an exact odd number of times. However, the definitive statement (see, for example, Chapter V in [1]) concerning members of W, namely that they have the form PQ2, where P is free of prime divisors p ≡ 3 (mod 4), was first given only in 1625 by the Dutch mathematician Albert Girard. It was also given a little later by Fermat, who probably had a proof of it, but the first published proof was by Euler in 1749.
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Acerbi, Fabio. "The meaning of πλασμαтιкόν in Diophantus’ Arithmetica". Archive for History of Exact Sciences 63, № 1 (2008): 5–31. http://dx.doi.org/10.1007/s00407-008-0028-8.

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Sasaki, Chikara. "D'al-Khwārizmī à Descartes." Arabic Sciences and Philosophy 23, no. 2 (2013): 319–25. http://dx.doi.org/10.1017/s0957423913000052.

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The volume D'al-Khwārizmī à Descartes is a monumental contribution to the world history of mathematical sciences, showing clearly that Arabic mathematics was an indispensable predecessor of early modern European mathematics. Roshdi Rashed is known, first of all, as an editor of classical mathematical writings in Arabic by such authors as al-Khwārizmī, Thābit ibn Qurra, Ibrāhīm ibn Sinān, Ibn al-Haytham, al-Khayyām, Sharaf al-Dīn al-Ṭūsī, as well as of the Arabic versions of Apollonius' Conics, Diophantus' Arithmetica, and Diocles' Burning Mirrors. As the volume under review shows, he is also a historian of mathematics of the first class who has transformed historiography. This book is, in a sense, a manifesto of Prof. Rashed's entire œuvre.
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Biase, Emanuele de. "The Vat. Gr. 191, Manuel Bryennius, and a circle of scholars alternative to that of Maximus Planudes." Scriptorium 70, no. 2 (2016): 349–63. http://dx.doi.org/10.3406/scrip.2016.4415.

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This article intends to give consistent answers to all the questions that a complex manuscript such as Vat. gr. 191 presents. All the descriptions hitherto published (and an autoptic examination) of this codex give a clear idea of the complexity of its genesis. After highlighting the inconsistencies found in the scientific contributions that aimed at identifying the revisor of this miscellany, this work presents all the information present in Vat. gr. 191 about the revisor, and then matches it with the profile of a prominent scholar of the time, Manuel Bryennius. This hypothesis finds further confirmation in the textual tradition of some of the texts contained in this manuscript, namely, Ptolemy’s Geographia and Diophantus’ Arithmetica.
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Cartiere, Carmelo R. "An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-quadratic Triples." Athens Journal of Education 12, no. 3 (2025): 527–46. https://doi.org/10.30958/aje.12-3-10.

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In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus’ “Arithmetica”, Pierre de Fermat stated that Diophantine equations of the Pythagorean form, , have no integer solutions for , and . Of this statement, however, Fermat never provided a proof. Only after more than 350 years, in 1994, Prof. Andrew J. Wiles was finally successful in demonstrating it (Wiles, 1995; Taylor & Wiles, 1995; Boston, 2008). However, Wiles’ proof adopts calculus techniques far beyond Fermat’s knowledge. Our aim is to show an analytical method to attempt a proof to Fermat’s last theorem with the only use of elementary calculus techniques. Keywords: number theory, Diophantine equations, Pythagorean Theorem, Fermat’s last theorem, numerical analysis
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Saliba, George. "Les arithmetiques. Diophante, Roshdi RashedBooks IV to VII of Diophantus' Arithmetica in the Arabic Translation Attributed to Qusta ibn Luqa. Diophantus, Jacques Sesiano." Isis 79, no. 2 (1988): 266–70. http://dx.doi.org/10.1086/354702.

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Knorr, Wilbur, and Jacques Sesiano. "Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qusta Ibn Luqa." American Mathematical Monthly 92, no. 2 (1985): 150. http://dx.doi.org/10.2307/2322659.

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Hogendijk, Jan P. "Books IV to VII of Diophantus' Arithmetica in the Arabic translation attributed to Qusṫā ibn Lūqā". Historia Mathematica 12, № 1 (1985): 82–85. http://dx.doi.org/10.1016/0315-0860(85)90077-1.

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Knorr, Wilbur. "Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qusṭâ Ibn Lûqâ. By Jacques Sesiano". American Mathematical Monthly 92, № 2 (1985): 150–54. http://dx.doi.org/10.1080/00029890.1985.11971565.

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Borić, Marijana. "Antički korijeni Getaldićeva rada na razvoju matematičke analize i sinteze." Radovi Zavoda za hrvatsku povijest Filozofskoga fakulteta Sveučilišta u Zagrebu 52, no. 1 (2020): 95–120. http://dx.doi.org/10.17234/radovizhp.52.4.

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The diverse opus of Marin Getaldić can methodologically and conceptually be divided into two parts. Getaldić’s early works can be considered as a reinterpretation of selected works from the ancient Greek and Roman tradition with the aim of transmitting ancient knowledge and theories, but also as an effort to further explore and improve these teachings within the framework of ancient Greek mathematical methods. In his more mature works, Getaldić was focused on the problem of the method. For twenty years, in his native Dubrovnik, he was developing the ideas he had encountered on a study trip across Europe, independently and almost completely isolated from the intense developments in the European scientific community in the first decades of the 17th century. He summarized the findings of his research in a seminal, five-volume work De resolutione et compositione mathematica (Rome 1630). Although Getaldić operated in an environment that was permeated by the Renaissance and humanist influences, in his local environment knowledge was transferred more slowly than in Western European countries where modern science emerged during the 16th and 17th centuries. In Dubrovnik isolation, he created new theoretical and practical knowledge, as well as original works that echoed in the European scientific community not only during his lifetime, but also later, during the 17th and 18th centuries. His example shows that the transfer of knowledge did not take place only from European epistemological centers to the periphery, for it shows that the scientific transfers within Europe went in both directions. He worked at a time when the accumulated knowledge about ancient works and the spread of humanistic education outgrew the ancient tradition, and gradually, after the methodological transformation, modern science was founded and shaped. It took almost twenty centuries for the ancient mathematical methodology, complemented by knowledge assimilated from the Arab and Indian mathematical traditions, to be conceptually modified and new methods aiming at achieving new theoretical knowledge and practical solutions to be developed. In building his rich opus, Getaldić relied heavily on the original ancient mathematical methods, which he consistently applied to a variety of problems. His work was largely based on the works of Greek mathematicians, among whom Pappus and Diophantus stand out, and was influenced by Eudoxus’ theory of scale and Archimedes’ application of logical methodology, i.e. arithmetic interpretation of geometry. Getaldić combined different tendencies of ancient Greek mathematics in a unique and fruitful way. After mastering Viète’s symbolic algebra that operated with general quantities, Getaldić systematically explored the possibilities of symbolic algebra in relation to ancient mathematical methods, which played a crucial role in the further development of modern mathematics and gradually lead to another major conceptual change in mathematical history. The change did not only affect mathematics, but also enabled the emergence of new, simpler and more exact interpretations in other sciences as well.
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Dissertations / Theses on the topic "Problems of Diophantus' "Arithmetica""

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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.<br>Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
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Books on the topic "Problems of Diophantus' "Arithmetica""

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Little, Heath Thomas. Diophantus of Alexandria, a study in the history of Greek algebra: With a supplement containing an account of Fermat's theorems and problems connected with Diophantine analysis and some solutions of Diophantine problems by Euler. 2nd ed. Forgotten Books, 2011.

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Oaks, Jeffrey, and Jean Christianidis. Arithmetica of Diophantus: A Complete Translation and Commentary. Taylor & Francis Group, 2022.

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Oaks, Jeffrey A., and Diophantus. Arithmetica of Diophantus: A Complete Translation and Commentary. Routledge, 2022.

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Arithmetica of Diophantus: A Complete Translation and Commentary. Taylor & Francis Group, 2022.

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Oaks, Jeffrey, and Jean Christianidis. Arithmetica of Diophantus: A Complete Translation and Commentary. Taylor & Francis Group, 2022.

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Oaks, Jeffrey, and Jean Christianidis. Arithmetica of Diophantus: A Complete Translation and Commentary. Routledge, Chapman & Hall, Incorporated, 2022.

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Oaks, Jeffrey, and Jean Christianidis. Arithmetica of Diophantus: A Complete Translation and Commentary. Taylor & Francis Group, 2022.

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Sesiano, Jacques. Books IV to VII of Diophantus’ Arithmetica: In the Arabic Translation Attributed to Qustā ibn Lūqā. Springer, 2011.

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Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qustā ibn Lūqā. Springer, 2012.

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Sesiano, Jacques. Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qustā Ibn Lūqā. Springer, 2012.

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Book chapters on the topic "Problems of Diophantus' "Arithmetica""

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Christianidis, Jean, and Jeffrey Oaks. "Numbers, problem solving, and algebra." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-3.

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Christianidis, Jean, and Jeffrey Oaks. "Diophantus and his work." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-2.

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Christianidis, Jean, and Jeffrey Oaks. "Book VII (Arabic)." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-25.

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Christianidis, Jean, and Jeffrey Oaks. "Book VI (Arabic)." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-24.

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Christianidis, Jean, and Jeffrey Oaks. "Book VI (Arabic)." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-13.

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Christianidis, Jean, and Jeffrey Oaks. "Book V (Arabic)." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-23.

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Christianidis, Jean, and Jeffrey Oaks. "Book II." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-9.

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Christianidis, Jean, and Jeffrey Oaks. "Book VIG." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-28.

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Christianidis, Jean, and Jeffrey Oaks. "History." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-4.

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Christianidis, Jean, and Jeffrey Oaks. "Book VIG." In The Arithmetica of Diophantus. Routledge, 2022. http://dx.doi.org/10.4324/9781315171470-17.

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Conference papers on the topic "Problems of Diophantus' "Arithmetica""

1

Avdyev, Marat Aleksandrovich. "Fermat's Last Theorem and ABC-Conjecture in the School of the XXI Century." In International Scientific and Practical Conference. TSNS Interaktiv Plus, 2024. http://dx.doi.org/10.21661/r-561630.

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In 1637, Pierre de Fermat wrote at the margins of Diophantus’ Arithmetica that he had found a truly wonderful proof of the insolvability of the Diophantine equation a^n + b^n = c^n, where n &amp;gt; 2, but the narrow margins of the books did not allow him to give the full proof. Is there a short and easy way to prove Fermat's Last Theorem? The following ABC conjecture states that for three co-prime numbers A, B, and C which satisfy A + B = C, the product of the prime factors of ABC is usually not much less than C. Both theorems are formulated very simply, but are extremely difficult to prove. Hundreds of pages have been spent by eminent mathematicians of Western world searching for proofs, and the search for proofs continues. The author found new methods of proof that are generally understandable, even to schoolchildren on the basis of a synthesis of several sciences, including physics. Number theory plays an interesting role in pedagogy.
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Journal articles
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