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On the Solutions of Two Diophantine Equations n^2x +2^y=z^2 and n^2x-2^y=z^2 |
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| รหัสดีโอไอ | |
| Creator | Suton Tadee |
| Title | On the Solutions of Two Diophantine Equations n^2x +2^y=z^2 and n^2x-2^y=z^2 |
| Contributor | Chantana Wannaphan |
| Publisher | Faculty of Science, Ubon Ratchathani University |
| Publication Year | 2565 |
| Journal Title | Journal of Science and Science Education |
| Journal Vol. | 5 |
| Journal No. | 2 |
| Page no. | 65-69 |
| Keyword | Diophantine equation, non-negative integer solution |
| URL Website | https://so04.tci-thaijo.org/index.php/JSSE |
| Website title | Journal of Science and Science Education |
| ISSN | ISSN 2697-410X |
| Abstract | In this paper, we show that all non-negative integer solutions of the Diophantine equation n^2x +2^y=z^2 where n is an odd positive integer, are of the following form. (n,x,y,z)?{(1,a,3,3)?a?Z,a?0}?{(b,0,3,3)?b?Z,b>1}? {(2^(c-2)-1,1,c,2^(c-2)+1) ?c?Z,c>3}.All non-negative integer solutions of the Diophantine equation n^2x-2^y=z^2 where n is an odd positive integer, are of the following form. (n,x,y,z)?{(1,d,0,0)? d?Z,d?0}?{(e,0,0,0)? e?Z,e>1}? {(2^(f-2)+1,1,f,2^(f-2)-1) ? f?Z,f>3}?{(3,1,3,1),(3,2,5,7)}. |
