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Computing Heights on Elliptic Curves
, 1988
"... ] C.J. Smyth. On measures of polynomials in several variables. Bull. Australian Math. Soc., 23:4963, 1981. Corrigendum: G. Myerson and C.J. Smyth, 26 (1982), 317319. [soule1991] C. Soul'e. Geometrie d'Arakelov et th'eorie des nombres transcendants. Ast'erisque, 198200:355371, 1991. [stewart ..."
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Cited by 29 (3 self)
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] C.J. Smyth. On measures of polynomials in several variables. Bull. Australian Math. Soc., 23:4963, 1981. Corrigendum: G. Myerson and C.J. Smyth, 26 (1982), 317319. [soule1991] C. Soul'e. Geometrie d'Arakelov et th'eorie des nombres transcendants. Ast'erisque, 198200:355371, 1991. [stewart1977] C.L. Stewart. On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers. Proceedings of the London Math. Soc., 35:425447, 1977. [stewart197778] C.L. Stewart. On a theorem of Kronecker and a related question of Lehmer. In S'eminaire de Th'eorie de Nombres Bordeaux 1977/78. Birkhauser, Basel, 1978. [stewart1978] C.L. Stewart. Algebraic integers whose conjugates lie near the unit circle. Bull. Soc. Math. France, 106:169176, 1978. [szydlo1985] B. Szydlo. An application of some theorems of G. Szegoe to Mahler measure of polynomials. Discuss. Math., 7:145148, 1985. [tatethesis]
A higher rank Mersenne problem
 ANTS V Proceedings, Springer Lecture Notes in Computer Science
"... Abstract. The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, ..."
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Cited by 4 (2 self)
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Abstract. The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, in both a classical and an elliptic setting. Numerical evidence is presented for both cases, and some of the difficulties involved in developing even a heuristic understanding of the problem are discussed. 1.
DISTRIBUTED PRIMALITY PROVING AND THE PRIMALITY OF (2^3539+ 1)/3
, 1991
"... We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the lO65digit (2^3539+ l)/3, the fir ..."
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Cited by 2 (1 self)
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We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the lO65digit (2^3539+ l)/3, the first ordinary Titanic prime.
Journal of Integer Sequences, Vol. 13 (2010), Article 10.1.7 On a Compositeness Test for (2 p + 1)/3
"... In this note, we give a necessary condition for the primality of (2 p + 1)/3. 1 ..."
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In this note, we give a necessary condition for the primality of (2 p + 1)/3. 1