On the Diophantine Equations x^2+y^2+z^2=kxyz

dc.contributor洪有情zh_TW
dc.contributorYu-Ching Hungen_US
dc.contributor.author林志穎zh_TW
dc.contributor.authorChih-Ying Linen_US
dc.date.accessioned2019-09-05T01:13:20Z
dc.date.available2007-7-4
dc.date.available2019-09-05T01:13:20Z
dc.date.issued2007
dc.description.abstract這篇論文中,我們就k值來探討丟番圖方程x^2+y^2+z^2=kxyz之解的情形: (1)當k不為1和3時,此方程式無正整數解。 (2)當k=1時,有無限多組正整數解。若將解表為(a,b,c),a小於或等於b小 於或等於c,則 ① 當c=3p^n或c=6p^n時,有解必唯一。 ② 若c為奇數,當c-2=p^n或c+2=p^n時,有解必唯一。 ③ 若c為偶數,當c-2=4p^n或c+2=8p^n時,有解必唯一。 (3)當k=3時,即為大家熟知的馬可夫方程式。zh_TW
dc.description.abstractIn this paper, we discuss the positive integers solutions of the Diophantine equations x^2+y^2+z^2=kxyz. (1)When k doesn't equal to 1 and 3, the equations have no positive integers solutions. (2)When k=1, the equation has infitely many positive integers solutions. We can let (a,b,c) be the solution and arrange its entries in ascending order. ①The solution is determined uniquely by c when c=3p^n or c=6p^n. ②If c is odd, the solution is determined uniquely by c when c-2=p^n or c+2=p^n . ③If c is even, the solution is determined uniquely by c when c-2=4p^n or c+2=8p^n. (3)When k=3, it is the well known Markoff equation.en_US
dc.description.sponsorship數學系zh_TW
dc.identifierGN0694400022
dc.identifier.urihttp://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN0694400022%22.&%22.id.&
dc.identifier.urihttp://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101736
dc.language英文
dc.subject馬可夫方程式zh_TW
dc.subjectMarkoff Equationen_US
dc.titleOn the Diophantine Equations x^2+y^2+z^2=kxyzzh_TW

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