关于不定方程x^3+y^3+z^3+w^3=n

On the Diophantine Equation x^3+y^3+z^3+w^3=n

对于不定方程x3+y3+z3+w3=n,证明了:当n=18k±1或n=18k±7或n=18k±8或n=6k±3时,它有无穷多组整数解,这里k为任意整数.

This paper deals with the Diophantine equation x3＋y3＋z3＋w2=n.It is proved that the Diophantine equation has infinitely many integral solutions,when n=18k±1 or n=18k±7 or n=18k±8 or n=6k±3,where k is an tnteger.