Integers representable by (x+y+z)3/xyz
In [1], A. Bremner and R. K. Guy discuss the problem of findin8 integers which may be represented by (x+y+z)3/xyz where X,Y,Z are integers. To this end, they present tables of solutions for integers n in the range −200≤n≤200 and offer several parametric solutions which involve both positive and nega...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000143 |
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| _version_ | 1832545487071215616 |
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| author | Sharon A. Brueggeman |
| author_facet | Sharon A. Brueggeman |
| author_sort | Sharon A. Brueggeman |
| collection | DOAJ |
| description | In [1], A. Bremner and R. K. Guy discuss the problem of findin8 integers which may
be represented by (x+y+z)3/xyz where X,Y,Z are integers. To this end, they present tables of
solutions for integers n in the range −200≤n≤200 and offer several parametric solutions which
involve both positive and negative integers. We present four infinite families of solutions which
involve only positive intesers. Furthermore, these families contain sequences that are generated
by linearly recursive relations. |
| format | Article |
| id | doaj-art-18dda2afe2b6472cbdca987e11108e25 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-18dda2afe2b6472cbdca987e11108e252025-02-03T07:25:41ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121110711510.1155/S0161171298000143Integers representable by (x+y+z)3/xyzSharon A. Brueggeman0Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana 61801, IL, USAIn [1], A. Bremner and R. K. Guy discuss the problem of findin8 integers which may be represented by (x+y+z)3/xyz where X,Y,Z are integers. To this end, they present tables of solutions for integers n in the range −200≤n≤200 and offer several parametric solutions which involve both positive and negative integers. We present four infinite families of solutions which involve only positive intesers. Furthermore, these families contain sequences that are generated by linearly recursive relations.http://dx.doi.org/10.1155/S0161171298000143 |
| spellingShingle | Sharon A. Brueggeman Integers representable by (x+y+z)3/xyz International Journal of Mathematics and Mathematical Sciences |
| title | Integers representable by
(x+y+z)3/xyz |
| title_full | Integers representable by
(x+y+z)3/xyz |
| title_fullStr | Integers representable by
(x+y+z)3/xyz |
| title_full_unstemmed | Integers representable by
(x+y+z)3/xyz |
| title_short | Integers representable by
(x+y+z)3/xyz |
| title_sort | integers representable by x y z 3 xyz |
| url | http://dx.doi.org/10.1155/S0161171298000143 |
| work_keys_str_mv | AT sharonabrueggeman integersrepresentablebyxyz3xyz |