Zhao Tian
Abstract
In this paper,the author has proved that the Diophantine equation x3+64=21y2 has only an integer solution(x,y)=(-4,0),(5,±3) and then gives all integer solution of x3+64=21y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residue.
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In this paper,the author has proved that the Diophantine equation x3+64=21y2 has only an integer solution(x,y)=(-4,0),(5,±3) and then gives all integer solution of x3+64=21y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residue.
Key concepts: Diophantine equation, Legendre's equation, Diophantine set, Integer (computer science), Mathematics, Quadratic residue, Quadratic equation, Sequence (biology)