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On the existence and non-existence of elliptic pseudoprimes
2009
Mathematics of Computation
In a series of papers, D. Gordon and C. Pomerance demonstrated that pseudoprimes on elliptic curves behave in many ways very similar to pseudoprimes related to Lucas sequences. In this paper we give an answer to a challenge that was posted by D. Gordon in 1989. The challenge was to either prove that a certain composite N ≡ 1 mod 4 did not exist, or to explicitly calculate such a number. In this paper, we both present such a specific composite (for Gordon's curve with CM by Q( √ −7)), as well as
doi:10.1090/s0025-5718-09-02275-3
fatcat:sp3aw2w2zjcvte4ydpazri5wle