Ljunggren proved that the equations x^3+1=Dy^2, D】2, d|D, 3D, d is not a square (1) and x^3-1=Dy^2, d is not prime of the form 6l+1 (1)′have one positive integral solution at most. Ko Chao and Sun Chi proved that eq...Ljunggren proved that the equations x^3+1=Dy^2, D】2, d|D, 3D, d is not a square (1) and x^3-1=Dy^2, d is not prime of the form 6l+1 (1)′have one positive integral solution at most. Ko Chao and Sun Chi proved that eqs.(1) and(1)′both have no nontrivial integral solution. In this letter, we prove the following theorems.展开更多
Mordell asked for the integer solutions of(1/x)+(1/y)+(1/z)+(1/w)+(1/xyxw)=0.(1)In this paper,we give some parametrio solutions of (1)and prove that thegeneral equationsum form i=1 to n(1/x)i)+multiply from i=1 to n=1...Mordell asked for the integer solutions of(1/x)+(1/y)+(1/z)+(1/w)+(1/xyxw)=0.(1)In this paper,we give some parametrio solutions of (1)and prove that thegeneral equationsum form i=1 to n(1/x)i)+multiply from i=1 to n=1(n>1)(2)展开更多
文摘Ljunggren proved that the equations x^3+1=Dy^2, D】2, d|D, 3D, d is not a square (1) and x^3-1=Dy^2, d is not prime of the form 6l+1 (1)′have one positive integral solution at most. Ko Chao and Sun Chi proved that eqs.(1) and(1)′both have no nontrivial integral solution. In this letter, we prove the following theorems.
文摘Mordell asked for the integer solutions of(1/x)+(1/y)+(1/z)+(1/w)+(1/xyxw)=0.(1)In this paper,we give some parametrio solutions of (1)and prove that thegeneral equationsum form i=1 to n(1/x)i)+multiply from i=1 to n=1(n>1)(2)
