Guan Xun-gui
Abstract
Let p be an odd prime,and this paper proves the following: if p=6(4s+2)+1,where s is a nonnegative integer,then the equation x3-1=2py2 has only integer solution(x,y)=(1,0);if p=6(4s+2)+1,where s is a nonnegative integer,then the equation x3+1=2py2 has only integer solution(x,y)=(-1,0).
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Let p be an odd prime,and this paper proves the following: if p=6(4s+2)+1,where s is a nonnegative integer,then the equation x3-1=2py2 has only integer solution(x,y)=(1,0);if p=6(4s+2)+1,where s is a nonnegative integer,then the equation x3+1=2py2 has only integer solution(x,y)=(-1,0).
Key concepts: Diophantine equation, Integer (computer science), Mathematics, Radical of an integer, Prime factor, Prime (order theory), Combinatorics, Diophantine set