关于丢番图方程x^6±y^6=2pz^2

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

设p>3为素数,证明了丢番图方程x6-y6=2pz2无正整数解,证明了丢番图方程x6+y6=2pz2在p 1(mod24)时无正整数解,同时获得了方程在p≡1(mod24)时有正整数解的计算公式.

Let p>3 be a prime integer prime,when the elementary grade method and the Diophantus Equation theories are used.It proves that the equation x^6-y^6=2pz^2 has not the positive integer solution,and the equation x^6+y^6=2pz^2 (p1(mod 24)) has not the positive integer solution.If the equation has the solution,the P must be like this:p>3 and p≡1(mod 24) and it also builds up the relative formula.