丢番图方程x3+1=PQy2的整数解
Integer Solution of the Diophantine Equation x3+1=PQy2
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摘要: 利用同余式、递归序列、勒让德符号、Pell方程的解的性质证明了p≡19(mod 24)为奇素数，q=73，97，241，337，409，\left (\fracpq\right)=-1时，丢番图方程x3+1=PQy2仅有整数解(x，y)=(-1，0)．Abstract: In our report,congruence,recurrent sequence,Legendre symbol,and some properties of the solutions to Pell equation were used to prove that the Diophantine equation x3+1=PQy2 only has integer solution (x,y)=(1,0),when p is odd prime with p≡19(mod 24),q=73,97,241,337,409,and \left(\fracpq\right)=-1
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