【摘要】 用初等方法给出了丢番图方程2x-2y.3z-4.3w=3.9k+1,x>0,y>0,z≥0,w≥0,k>0的全部整数解,利用这一结果,推出与和完全数有关的一类不定方程仅有一组整数解.更多还原

【Abstract】 By using elementary method,all of the integer solutions of the Diophantine equation 2x-2y·3z-4·3w=3·9k+1,where x,y,k>0,z,w≥0 are obtained as follows:(x,y,z,w,k)=(6,3,1,1,1),(7,6,0,2,1)(8,3,3,1,1),(8,6,1,2,1),(9,8,0,1,2),(10,3,1,5,1),(10,8,1,1,2),(12,7,2,6,1),(6,5,0,0,1),(7,5,1,0,1),(8,3,0,0,2)Based on that,all of the integer solutions of the Diophantine equation2a+c+2-2c+2·3d+f+k-2-4·3f+k-1=3k+1,a>0,c>0,d≥0,f≥0,k≡ 1(mod2)which is related to Perfect totient numbers,are given as(a,c,d,f,k)=(2,4,0,0,3).更多还原