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The Diophantine Equations of Second and Higher Degree of the Form 3xy = n (x + y) and 3xyz = n (xy + yz + zx) etc

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Author(s): Hari Kishan | Megha Rani | Smiti Agarwal

Journal: Asian Journal of Algebra
ISSN 1994-540x

Volume: 4;
Issue: 1;
Start page: 31;
Date: 2011;
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Keywords: Diophantine equation | conjecture and integral solution | unit fraction | Egyptian fraction | congruence modulo

ABSTRACT
In this study, the Diophantine equations of second and higher degree of the form 2xy = n (x + y), 3xy = n (x + y), 3xyz = n (xy + yz + xz), 4xyz = n (xy + yz + xz), 3wxyz = n (xyz + wyz + xyz + wxz) and 4vwxyz = n (wxyz + vxyz + vwyz + vwyz + vwxy), have been discussed. Congruence modulo relation has been used for solution part. Attempt has been made to obtain some positive integral solutions of these Diophantine equations.

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