关于不定方程 x^2+3y^(2p)=4z^2,2■z

On the Indefinite Equation x^2+3y^(2p)=4z^2,2■z

对于每个奇素数 p,求出了不定方程 x^2+3y^(2p)=4z^2满足 x>0,y>0,z>0,2■z 的全部有理整数解的表达式,这些表达式正好给出了不定方程 x^2+3y^(2p)=4(2z+1)满足 x>0,y>0,z>0且(2z+1)为完全平方数的那些有理整数解.后一个不定方程与 Fermat 猜想紧密相关.

For every prime number P(P≥3),the expression of the whole rational integer solu- tions for the indefinite equation x^2+3y^(2p)=4z^2 satisfying x>0, y>0,z>0, 2■z was found out.The expression can give exactly the whole positive integer solutions of the e- quation x^2+3y^(2p)=4(2z+1)in the case that(2z+1)is a perfect square integer.There is a close correlation between the later equation and the Fermat′s conjecture.