关于不定方程X^nY^nZ^n=(X^n+Y^n)^(n+2)

Diophantine Equation x^ny^nz^n=((x^n+y^n))^(n+2)

根据费马大定理,运用基础数论的方法,证明了不定方程xnynzn=(xn+yn)n+2,(n 3)没有正整数解.

According to the Fermat＇s Last Theorem,the Elementary Number, the anthors proved the diophantine equation x^ny^nz^n=（x^n＋y^n）^n＋2（ n ≥3 ） has no positive integer solution by using the Elementary Number Theory. Theory is used to work out that the diophantine equation xx^ny^nz^n=（x^n＋y^n）^n＋2（≥3） has no positive ingeger solution in this thesis.