INTEGRAL SOLUTIONS OF THE TERNARY CUBIC EQUATION

S. Vidhyalakshmi, T.R. UshaRani, M.A.Gopalan

Abstract: The ternary cubic equation 2 2 3 5(x ? y ) ? 9xy ? x ? y ?1 ? 35z is considered for determining its non-zero distinct integral solutions Employing the linear transformations x=u+v,y=u-v (u?v?0),and employing the meyhod of factorization in complex conjugates, different patterns of integral solutions to the ternary cubic equation under consideration are obtained.. In each pattern, interesting relations among the solutions, some special polygonal , pyramidal numbers and central pyramidal numbers are exhibited.

Keywords: Ternary cubic, Integral solutions, polygonal number, pyramidal number, Mathematics subject classificationnumber: 11D09

DOI: https://doi.org/10.15623/ijret.2014.0311076