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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| Format: | Article |
| Language: | English |
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Hindawi Limited
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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doaj-7d6d0d5d82664692bd2c2c3c10d757c92020-11-24T21:06:30ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuanyuan Deng Wenpeng Zhang |
| spellingShingle |
Yuanyuan Deng Wenpeng Zhang On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz Abstract and Applied Analysis |
| author_facet |
Yuanyuan Deng Wenpeng Zhang |
| author_sort |
Yuanyuan Deng |
| title |
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_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_sort |
on the odd prime solutions of the diophantine equation xy+yx=zz |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2014/186416 |
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AT yuanyuandeng ontheoddprimesolutionsofthediophantineequationxyyxzz AT wenpengzhang ontheoddprimesolutionsofthediophantineequationxyyxzz |
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