• Ramanand Raman

A cubic surface is a projective variety studied in algebraic geometry. It is an algebraic surface in three-dimensional projective space. Cubic surfaces defined over the field of rational numbers often contain infinitely many rational points. In this present paper, we discuss the rational points on cubic surfaces. No method is known for determining whether rational points exist on a general cubic surface F(x, y, z) = 0, or for finding all of them if any exist. Geometric considerations may help in finding infinite solutions and even all the solutions for cubic surfaces.

Diophantine equation, cubic surface, cubic polynomial, rational point, rational coefficient, rational number

"RATIONAL POINTS ON CUBIC SURFACES", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 4, page no.17-20, April-2019, Available :http://www.jetir.org/papers/JETIR1904H05.pdf

"RATIONAL POINTS ON CUBIC SURFACES", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 4, page no. pp17-20, April-2019, Available at : http://www.jetir.org/papers/JETIR1904H05.pdf