【摘要】 利用初等数论方法及Fermat无穷递降法,证明了丢番图方程x~4+my~4=z~4,在m=12,-48,42,-168时均无正整数解;在m=-12,-42,48,168时均有无穷多组正整数解,并进一步得出了其解的通解公式,从而获得了Tijdeman猜想与广义Fermat猜想的进一步结果。更多还原

【Abstract】 With the use of approach of elementary number theory and Fermat’s infinite decrease by degrees, it proves that if m = 12, -48, 42, -168, the diophantine equation X4 + mY4 = Z2 has no positive integer solutions; if m = -12, -42, 48, 168, then the equation has infinite integer solutions. And we can also draws its solutions’ common formula, and gets the further results of Tijdeman’s conjecture and the General Fermat’s conjecture更多还原