An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-Quadratic Triples
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| Title: | An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-Quadratic Triples |
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| Language: | English |
| Authors: | Carmelo R. Cartiere |
| Source: | Athens Journal of Education. 2025 12(3):527-546. |
| Availability: | Athens Institute for Education & Research. 8 Valaoritou Street, Kolonaki, Athens 10671, Greece. e-mail: education@atiner.gr; Web site: https://www.athensjournals.gr/aje |
| Peer Reviewed: | Y |
| Page Count: | 20 |
| Publication Date: | 2025 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Mathematics Education, Calculus, Validity, Mathematical Logic, History, Mathematics, Equations (Mathematics), Problem Solving |
| ISSN: | 2407-9898 2241-7958 |
| Abstract: | 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, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. 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. |
| Abstractor: | As Provided |
| Entry Date: | 2025 |
| Accession Number: | EJ1480305 |
| Database: | ERIC |
| Abstract: | 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, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. 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. |
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| ISSN: | 2407-9898 2241-7958 |
