关于不定方程x^(2p)+y^(2p)=z^(2p)

On Indefinite Equation x 2p +y 2p =z 2p

素数ｐ＞３，证明了若ｘ、ｙ、ｚ满足不定方程ｘ２ｐ＋ｙ２ｐ＝ｚ２ｐ，则８ｐ２｜ｘ；ｚ＝１＋８ｚ１；ｙ＝１＋８ｙ１或ｙ＝７＋８ｙ１；ｙｐ－１＝１＋ｌ０ｐ２；

This paper proves that if x,y and z satisfy the indefinite equation x 2p +y 2p =z 2p ,where the prime number p >3,then the following conclusion exist: 8 p 2|x;\ z=1+8z 1,\ y=1+8y 1 or y=7+8y 1;\ y p-1 =1+l 0p 2, z p-1 =1+l 1p 2