OBSERVATIONS ON THE NON- HOMOGENEOUS QUINTIC EQUATION WITH FIVE UNKNOWNS
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1 OBSERVATIONS ON THE NON- HOMOGENEOUS QUINTIC EQUATION WITH FIVE UNKNOWNS y z w P S.Vidhylhmi S.Mlli M.A.Gopl Aitt Profeor of Mthemtic SIGC Trichy-TmildIdi Lectrer of Mthemtic SIGC Trichy-TmildIdi Aitt Profeor of Mthemtic SIGC Trichy-TmildIdi Atrct: The qitic Diophtie eqtio with five ow y z w p i lyzed for it ifiitely my o-zero ditict itegrl oltio. A few iteretig reltio etwee the oltio d pecil mer mely cetered polygol mer cetered pyrmidl mer jcothl mer Lc mer d Keye mer re preeted. Keyword: Qitic eqtio with five ow Itegrl oltio cetered polygol mer cetered pyrmidl mer. Mthemtic ject clifictio mer: D. t m NOTATIONS m - Polygol mer of r with ize m. P m m 5 m 6 - Pyrmidl mer of r with ize m. Pt - Pettope mer of r SO -Stell octglr mer of r S 6 -Str mer of r Pr - Proic mer of r. Copyright to IJIRSET 6
2 J -Jcothl mer of r. j - Jcothl lc mer of r. Ky - Keye mer. F m F5 m! whoe geertig polygo i trigle. 5! -For dimeiol figrtive mer of r r whoe geertig polygo i trigle. m -Five dimeiol figrtive mer of CP m - Cetered polygol mer of r with ize m. I.INTRODUCTION The theory of Diophtie eqtio offer rich vriety of fcitig prolem. I prticlr qitic eqtio homogeeo or o-homogeeo hve roed the iteret of mero mthemtici ice tiqity.for illtrtio oe my refer -0for qitic eqtio with three for d five ow. Thi pper cocer with the prolem of determiig itegrl oltio of the o-homogeeo qitic eqtio with five ow give y y z w p A few reltio etwee the oltio d the pecil mer re preeted... II.METHOD OF ANALYSIS The Diophtie eqtio repreetig the qitic with five ow der coidertio i y z w p Itrodcig the trformtio v y v z v w v where i ditict poitive ditict iteger i we get v p Ame p Copyright to IJIRSET 7
3 Copyright to IJIRSET 8 Stittig i d employig the method of fctoriztio defie i i i iv 5 eqtig rel d imgiry prt we get v Th i view of the o-zero ditict itegrl oltio of re give y y z w p.for implicity d cler dertdig we preet elow the iteger oltio d the correpodig propertie for 0 d. A. Ce: Let 0 The o-zero ditict iteger oltio of re fod to e y z w p
4 B.Propertie y OH S 7 Pr t 0mod p Ky 6J 0 y Cp6 6P t t5 6 t6. p Ky 0mod 5 6 y p SO S 5 Pr 5 8 t t5 i ty mer Remr : It i worth to ote tht whe 0 we hve other ptter of oltio which i illtrted elow. For thi ce 0 redce to v p 6 Followig the lyi preeted ove the vle of d v re give y v Hece the o-zero ditict itegrl oltio of re give y y z w p The ove vle of y z d w re differet from tht of i ce preeted ove. C.Propertie: y P t CP S 0mod. Copyright to IJIRSET 9
5 P SO t t p P So i ty mer. y OH 8t P t 0mod. 5 p 8Pt 6P S 6t 0 D.Ce: Let.After performig few clcltio i ce the o-zero ditict iteger oltio re otied E.Propertie: y z w p 5 y P Pr t CP6 6t 5 t 0. y P S SO t8 0mod p Ky j whe 0 III.CONCLUSION I dditio to the ove ptter of oltio there re other form of iteger oltio to. For illtrtio the eqtio 6 i writte v p * 7 Write Copyright to IJIRSET 0
6 m im m im m 8 or m i m m i m m 9 Uig d 8 i 7 d employig the method of fctoriztio defie m im iv i i m Eqtig the rel d imgiry prt the vle of d v re otied.sttig thee vle of d v i d chooig d itly my differet iteger oltio to re otied. Similr proce i crried ot y coiderig d 9. To coclde oe my erch for other choice of oltio to log with the correpodig propertie. REFERENCES. L.E.Dico Hitory of Theory of Nmer Vol. Chele Plihig compy New Yor 95. L.J.Mordell Diophtie eqtio Acdemic Pre Lodo969. Crmichel R.D.The theory of mer d Diophtie AlyiDover Plictio New Yor 959 M.A.Gopl & A.Vijyhr A Iteretig Diophtie prolem 5 Developmet d Egieerig Applictio Nro Plihig Hoe Pp M.A.Gopl & A.Vijyhr Itegrl oltio of terry qitic Diophtie eqtio y z Advce i Mthemtic Scietific 5 y z Itertiol Jorl of Mthemticl Sciece j-je 00 6 M.A.GoplG.Smthi & S.Vidhylhmi Itegrl oltio of o-homogeeo terry qitic eqtio i term of pell 5 eqece y y y Z ccepted for Plictio i JAMSReerch Idi Plictio 7. S.Vidhylhmi K.Lhmi d M.A.Gopl Oervtio o the homogeeoqitic eqtio with for ow y z 5 y y w ccepted for Plictio i Itertiol Jorl of Mltidicipliry Reerch Acdemy IJMRA. 8 M.A.Gopl & A.Vijyhr Itegrl oltio of o-homogeeo qitic eqtio with five ow Beel J.Mth M.A.Gopl & A.Vijyhr oltio of qitic eqtio with five ow 5 y zw R y z w P Accepted for Plictio i Itertiol Review of Pre d Applied Mthemtic. 0 M.A.Gopl G. Smthi & S.Vidhylhmi O the o-homogeo qitic eqtio with five ow y z w 6T 5 ccepted for Plictio i Itertiol Jorl of Mltidicipliry Reerch Acdemy IJMRA. Copyright to IJIRSET
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