Journal of the Ramanujan Mathematical Society

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A Diophantine Equation of Mordell


Affiliations
1 Foreign Service Institute, Old J. N. U. Campus, Baba Gang Nath Marg, New Delhi-110067, India
     

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While one- and two-parameter solutions of the diophantine equation 1/x+1/y+1/z+1/w+1/xyzw=0 are known and all integer solutions below a given bound can also be obtained, the complete solution of this equation has not yet been found. The published parametric solutions generate integer solutions of a somewhat restricted type. In this paper we obtain much more general, infinitely many, two-parameter solutions of the aforesaid equation. We also show how even more general, infinitely many, solutions expressed in terms of several parameters can be obtained.
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  • A Diophantine Equation of Mordell

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Authors

Ajai Choudhry
Foreign Service Institute, Old J. N. U. Campus, Baba Gang Nath Marg, New Delhi-110067, India

Abstract


While one- and two-parameter solutions of the diophantine equation 1/x+1/y+1/z+1/w+1/xyzw=0 are known and all integer solutions below a given bound can also be obtained, the complete solution of this equation has not yet been found. The published parametric solutions generate integer solutions of a somewhat restricted type. In this paper we obtain much more general, infinitely many, two-parameter solutions of the aforesaid equation. We also show how even more general, infinitely many, solutions expressed in terms of several parameters can be obtained.