On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz
Using the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation xy+yx=zz has no positive integer solutions (x,y,z) with x and y being odd primes.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/186416 |
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| _version_ | 1832550983531495424 |
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| author | Yuanyuan Deng Wenpeng Zhang |
| author_facet | Yuanyuan Deng Wenpeng Zhang |
| author_sort | Yuanyuan Deng |
| collection | DOAJ |
| description | Using the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation
xy+yx=zz has no positive integer solutions (x,y,z) with x and y being odd primes. |
| format | Article |
| id | doaj-art-7d6d0d5d82664692bd2c2c3c10d757c9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7d6d0d5d82664692bd2c2c3c10d757c92025-02-03T06:05:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/186416186416On the Odd Prime Solutions of the Diophantine Equation xy+yx=zzYuanyuan Deng0Wenpeng Zhang1School of Mathematics, Northwest University, Xi’an, Shaanxi 710127, ChinaSchool of Mathematics, Northwest University, Xi’an, Shaanxi 710127, ChinaUsing the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation xy+yx=zz has no positive integer solutions (x,y,z) with x and y being odd primes.http://dx.doi.org/10.1155/2014/186416 |
| spellingShingle | Yuanyuan Deng Wenpeng Zhang On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz Abstract and Applied Analysis |
| title | On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz |
| title_full | On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz |
| title_fullStr | On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz |
| title_full_unstemmed | On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz |
| title_short | On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz |
| title_sort | on the odd prime solutions of the diophantine equation xy yx zz |
| url | http://dx.doi.org/10.1155/2014/186416 |
| work_keys_str_mv | AT yuanyuandeng ontheoddprimesolutionsofthediophantineequationxyyxzz AT wenpengzhang ontheoddprimesolutionsofthediophantineequationxyyxzz |