See also Atkin-Goldwasser-Kilian-Morain Certificate ,
Elliptic Curve Primality
Proving ,
Strong Elliptic Pseudoprime
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References Balasubramanian, R. and Murty, M. R. "Elliptic Pseudoprimes. II." In Séminaire
de Théorie des Nombres, Paris 1988-1989 Gordon, D. M. "The
Number of Elliptic Pseudoprimes." Math. Comput. 52 , 231-245, 1989. Gordon,
D. M. "Pseudoprimes on Elliptic Curves." In Number
Theory--Théorie des nombres:Proceedings of the International Number Theory
Conference Held at Université Laval in 1987 Miyamoto,
I. and Murty, M. R. "Elliptic Pseudoprimes." Math. Comput. 53 ,
415-430, 1989. Ribenboim, P. The
New Book of Prime Number Records, 3rd ed. Referenced on Wolfram|Alpha Elliptic Pseudoprime
Cite this as:
Weisstein, Eric W. "Elliptic Pseudoprime."
From MathWorld https://mathworld.wolfram.com/EllipticPseudoprime.html
Subject classifications
be an elliptic curve defined over the field
of rationals 
having equation
and 
integers. Let 
be a point on 
with integer coordinates and having infinite order in the
additive group of rational points of 
, and let 
be a composite natural
number such that 
, where 
is the Jacobi symbol.
Then if
is called an elliptic pseudoprime for 
.
