Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem
The present study aims to develop novel parametric solutions for the Prouhet Tarry Escott problem of second degree with sizes 3, 4 and 5. During this investigation, new parametric representations for integers as the sum of three, four and five perfect squares in two distinct ways are identified. Mor...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1775 |
| _version_ | 1797550997426405376 |
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| author | Srikanth Raghavendran Veena Narayanan |
| author_facet | Srikanth Raghavendran Veena Narayanan |
| author_sort | Srikanth Raghavendran |
| collection | DOAJ |
| description | The present study aims to develop novel parametric solutions for the Prouhet Tarry Escott problem of second degree with sizes 3, 4 and 5. During this investigation, new parametric representations for integers as the sum of three, four and five perfect squares in two distinct ways are identified. Moreover, a new proof for the non-existence of solutions of ideal Prouhet Tarry Escott problem with degree 3 and size 2 is derived. The present work also derives a three parametric solution of ideal Prouhet Tarry Escott problem of degree three and size two. The present study also aimed to discuss the Fibonacci-like pattern in the solutions and finally obtained an upper bound for this new pattern. |
| first_indexed | 2024-03-10T15:38:30Z |
| format | Article |
| id | doaj.art-63f03d12bbb049888560caa352892410 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:38:30Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-63f03d12bbb049888560caa3528924102023-11-20T17:02:22ZengMDPI AGMathematics2227-73902020-10-01810177510.3390/math8101775Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott ProblemSrikanth Raghavendran0Veena Narayanan1Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, IndiaDepartment of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, IndiaThe present study aims to develop novel parametric solutions for the Prouhet Tarry Escott problem of second degree with sizes 3, 4 and 5. During this investigation, new parametric representations for integers as the sum of three, four and five perfect squares in two distinct ways are identified. Moreover, a new proof for the non-existence of solutions of ideal Prouhet Tarry Escott problem with degree 3 and size 2 is derived. The present work also derives a three parametric solution of ideal Prouhet Tarry Escott problem of degree three and size two. The present study also aimed to discuss the Fibonacci-like pattern in the solutions and finally obtained an upper bound for this new pattern.https://www.mdpi.com/2227-7390/8/10/1775Diophantine equationsProuhet Tarry Escott problemFibonacci pattern |
| spellingShingle | Srikanth Raghavendran Veena Narayanan Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem Mathematics Diophantine equations Prouhet Tarry Escott problem Fibonacci pattern |
| title | Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem |
| title_full | Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem |
| title_fullStr | Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem |
| title_full_unstemmed | Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem |
| title_short | Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem |
| title_sort | novel parametric solutions for the ideal and non ideal prouhet tarry escott problem |
| topic | Diophantine equations Prouhet Tarry Escott problem Fibonacci pattern |
| url | https://www.mdpi.com/2227-7390/8/10/1775 |
| work_keys_str_mv | AT srikanthraghavendran novelparametricsolutionsfortheidealandnonidealprouhettarryescottproblem AT veenanarayanan novelparametricsolutionsfortheidealandnonidealprouhettarryescottproblem |