关于丢番图方程x^6±y^6=3pz^2

On the Diophantine Equation x^6±y^6=3pz^2

设p>3是素数,该文运用数论方法证明了方程x6+y6=3pz2,x6±y6=6pz2均无正整数解,给出了方程x6-y6=3pz2有解的必要条件,并获得了相应的通解公式.

Let p>3 and p be prime number,we prove that if the Diophantine equation x^6+y^6=3pz^2,x^6±y^6=6pz^2 has not the positive integer solution.We give the necessary condition of the equation x^6-y^6=3pz^2,build up the relative formula.