Chinese Quarterly Journal of Mathematics ›› 2005, Vol. 20 ›› Issue (3): 242-246.

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Heron Triangle and Diophantine Equation

  

  1. Department of Mathematics, Aba Teacher's College, Wenchuan 623000, China
  • Received:2002-11-13 Online:2005-09-30 Published:2024-01-11
  • About author:YANG Shi-chun(1969-),male,native of Xichong,Sichuan,a lecturer of Aba Teacher's College, M.S.D.,engages in number theory;MA Chang-wei(1972 ),male(Huizu),native of Maoxian,Sichuan,a lecturer of Aba Teacher's College,M.S.D.,engages in mathematical analysis.
  • Supported by:
    Supported by the Natural Science Foundation of China(10271104);Supported by the Natural Science Foundation of Education Department of Sichuan Province(2004B25)

Abstract: In this paper,we  study  the  quantic  Diophantine  equation(1)with  elementary geometry method,therefore all positive integer solutions of the equation(1)are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.

Key words: quantic Diophantine equation, positive integer solution, Heron triangle, median 

CLC Number: