An Extension of Pythagorean Equation with Its Application—Pythagorean Equation and Special M-Gonal Numbers
Abstract: Based on the solution of Pythagorean Equation, we obtain a relationship that the difference be-tween two M-Gonal numbers is still an M-Gonal number. With this explicit computable expression, we establish a remarkable connection between two pairs of numbers. The projected planes of two pairs of numbers generate partial topological structure. In real Desarguesian projective plane, this structure shares many existing properties of topological ellipsoid naturally.
文章引用: 郭铭浩 , 郭志成 (2017) 勾股定理离散性质的推广和应用—Pythagorean方程和特殊的M角数。 理论数学， 7， 255-261. doi: 10.12677/PM.2017.74033
 Dickson, E.L. (2010) History of the Theory of Numbers. Diophantine Analysis, Vol. 2.
 Gopalan, M.A., Somanath, M. and Vanitha, N. (2007) M-Gonal Number – 1 = A Perfect Square. Acta Ciencia Indica Mathematics, Vol XXXIII M, 479-480.
 Bhanumathy, T.S. (1995) Ancient Indian Mathematics. New Age Publishers Ltd, New Delhi.
 Gopalan, M.A., Somanath, M. and Vanitha, N. (2009) On pairs of M-Gonal Numbers with Unit Difference. Reflections des ERA-JMS, 4, 365-376.
 Gopalan, M.A., Geetha, K. and Somanath, M. (2014) M-Gonal Number, ±2 = A Perfect Square. International Journal of Innovative Technology and Research, 2, 1618-1620.
 Gopalan, M.A. and Geetha, V. (2015) M-Gonal Number ±3 = A Perfect Square. International Journal of Mathematics Trends and Technology, 17, 32-35.
 Gopalan, M.A. and Devibala, S. (2006) Equality of Triangular Numbers with Special M-Gonal Numbers. Bulletin of Allahabad Mathematical Society, 21, 25-29.
Armstrong, M.A. (1983) Basic Topology. Undergraduate Texts in Mathematics, 137-155.
Polster, B., Rosehr, N. and Steinke, G.F. (1997) On the Existence of Topological Ovals in Flat Projective Planes. Archiv der Mathematik, 68, 418-429.