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arXiv 2014-01-02 0 views

Congruences for q[ᵖ/⁸] p II

Sun, Zhi-Hong

Original · EN

Let Z be the set of integers, and let p be a prime of the form 4k+1. Suppose q∈ Z, 2 q, p q, p=c²+d², c,d∈ Z and c≡ 1 4. In this paper we continue to discuss congruences for q[ᵖ/⁸] p and present new reciprocity laws, but we assume 4p=x²+qy² or p=x²+2qy², where [·] is the greatest integer function and x,y∈ Z.

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