| On the diophantine equation x
2 ? Dy
2 = n |
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| 作者姓名： | WEI DaSheng |
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| 作者单位： | Academy of Mathematics and Systems Science,Chinese Academy of Sciences |
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| 基金项目： | supported by National Natural Science Foundation of China(Grant No.10901150);the Deutsche Forschungsgemeinschaft(Grant No.DE 1646/2-1) |
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| 摘 要： | We propose a method to determine the solvability of the diophantine equation x2-Dy2=n for the following two cases:(1) D = pq,where p,q ≡ 1 mod 4 are distinct primes with(q/p)=1 and(p/q)4(q/p)4=-1.(2) D=2p1p2 ··· pm,where pi ≡ 1 mod 8,1≤i≤m are distinct primes and D=r2+s2 with r,s ≡±3 mod 8.
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| 关 键 词： | torus Hilbert class field reciprocity law |
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