几个不定方程在Q(√-3)中的解

摘要

By using Fermat's method of descent,this paper proved that Diophantine equations x~4-y~4=z~2 and x~4+4y~4=z~2 have no non-trivial solutions over Q(√-3),which implies that the Fermat Equation also has no non-trivial solutions in this field for n=4.%应用Femat下降法,证明了不定方程x~4-y~4=z~2与x~4+4y~4=~z2在Q(√-3)没有非平凡解,它表明Fermat方程当n=4时在此域中仍然没有非平凡解.