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Diofantska enačba mX [na] 2 - nY [na] 2 =[plus minus]1 : diplomsko delo
Vizjak, Mateja, 1985-
V prvem poglavju diplomskega dela zajamemo osnovne teorije verižnih ulomkov. Posebej opišemo končne, neskončne in periodične verižne ulomke. V drugem poglavju diplomskega dela obravnavamo Pellovo ...enačbo oz. diofantsko enačbo oblike X [na] 2 - dY [na] 2 = N, kjer je N = 1 in d tako naravno število, ki ni popoln kvadrat. Osrednji del je namenjen obravnavi diofantske enačbe oblike mX [na] 2 - nY [na] 2 =[plusminus]1, kjer opišemo vse pozitivne rešitve te diofantske enačbe in ugotovimo, da so slednje povezane z rešitvami Pellove enačbe R [na] 2 - mnS [na]2 = 1. Ena od glavnih ugotovitev pravi, da je diofantska enačba mX [na] 2 - nY [na] 2 =[plusminus]1 rešljiva natanko tedaj, ko je fundamentalna rešitev Pellove enačbe R [na] 2 - mnS [na] 2 = 1 kvadrat neke rešitve (x,y) enačbe mX [na] 2 - nY [na] 2 = 1. V zaključnem delu podrobno obravnavamo tiste rešitve (x [spodaj] i, y [spodaj] i) dotične diofantske enačbe, za katere velja, da vsi prafaktorji števila y [spodaj] i delijo tudi število n.
Type of material - undergraduate thesis
; adult, serious
Publication and manufacture - Maribor : [M. Vizjak], 2016
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