Volume : 6, Issue : 5, May - 2017

ON A DIOPHANTINE PROBLEM

A. Vijayasankar, M. A. Gopalan, V. Krithika

Abstract :

<p>&nbsp;<span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt; text-align: justify;">This paper aims at determining two non-zero distinct integers </span><span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt; text-align: justify;">< /> </span></p> <p><span style="font-size:12.0pt;line-height:115%;&#10;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:Calii;mso-ansi-language:&#10;EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter" /> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0" /> <v:f eqn="sum @0 1 0" /> <v:f eqn="sum 0 0 @1" /> <v:f eqn="prod @2 1 2" /> <v:f eqn="prod @3 21600 pixelWidth" /> <v:f eqn="prod @3 21600 pixelHeight" /> <v:f eqn="sum @0 0 1" /> <v:f eqn="prod @6 1 2" /> <v:f eqn="prod @7 21600 pixelWidth" /> <v:f eqn="sum @8 21600 0" /> <v:f eqn="prod @7 21600 pixelHeight" /> <v:f eqn="sum @10 21600 0" /> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect" /> <o:lock v:ext="edit" aspectratio="t" /> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style=‘width:15.75pt; height:17.25pt‘ o:ole=""> <v:imagedata src="file:///C:UsersFAIZMU~1AppDataLocalTempmsohtmlclip11clip_image001.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><img width="21" height="23" src="file:///C:/Users/FAIZMU~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" v:shapes="_x0000_i1025" alt="" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1558261680"> </o:OLEObject> </xml><![endif]-->and <span style="position:relative;top:5.0pt;mso-text-raise:&#10;-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style=‘width:17.25pt;height:17.25pt‘ o:ole=""> <v:imagedata src="file:///C:UsersFAIZMU~1AppDataLocalTempmsohtmlclip11clip_image003.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><img width="23" height="23" src="file:///C:/Users/FAIZMU~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png" v:shapes="_x0000_i1026" alt="" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1558261681"> </o:OLEObject> </xml><![endif]-->&nbsp;&nbsp;such that&nbsp;</span><span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt; position: relative; top: 5pt;"><img width="95" height="23" src="file:///C:/Users/FAIZMU~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" v:shapes="_x0000_i1025" alt="" /></span><span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt;">&nbsp;</span><span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt;">, </span><span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 12pt; position: relative; top: 5pt;"><img width="84" height="24" src="file:///C:/Users/FAIZMU~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png" v:shapes="_x0000_i1026" alt="" /><span style="font-size: 12pt;">&nbsp;</span></span></p>