| The main work of this paper was to study the existence and elementary solution of the positive integer solution of the Diophantine equation 1/x +1/y +1/z =1/3p,that p>3 is prime number.The main conclusion contained in this paper were as follows:1.It is proved the Diophantine equation 1/x +1/y+1/z=1/3p,(x＋y,z)=1 has no positive integer solution.2.It is obtained all positive integer solutions of the equation1/x+1/y+1/z=1/3p with d=(x y,z),(x/d,y/d),=(y/d,z/d)=(z/d,x/d)=13.It is obtained all positive integer solutions of the equation 1/x+1/y+1/z =1/3p with p|x,x≤y≤z.4.It is obtained all positive integer solutions of the Diophantine equation 1/x+1/y+1/z=1/1983... |
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