Using some elementary methods,such as congruence,Legendre symbol,recursive sequence,properties of the solutions of Pell equation,it is proved that whenp,Q are 6k+1 and 6k-1 odd prime numbers respectively or p,Q are two different 6k+1 odd prime numbers,the Diophantine equation x3+1=pQy2 has only integer solution(x,y)=(-1,0).
关键词
丢番图方程/整数解/同余/Legendre符号
Key words
Diophantine equation/Integer solution/Congruence/Legendre symbol
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