# The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve

Acta Arithmetica (1999)

- Volume: 88, Issue: 3, page 219-111
- ISSN: 0065-1036

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topJ. Cheon, and S. Hahn. "The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve." Acta Arithmetica 88.3 (1999): 219-111. <http://eudml.org/doc/207242>.

@article{J1999,

author = {J. Cheon, S. Hahn},

journal = {Acta Arithmetica},

keywords = {Bang's theorem; elliptic curves; reductions; local heights; Mordell-Weil groups; prime of good reduction},

language = {eng},

number = {3},

pages = {219-111},

title = {The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve},

url = {http://eudml.org/doc/207242},

volume = {88},

year = {1999},

}

TY - JOUR

AU - J. Cheon

AU - S. Hahn

TI - The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve

JO - Acta Arithmetica

PY - 1999

VL - 88

IS - 3

SP - 219

EP - 111

LA - eng

KW - Bang's theorem; elliptic curves; reductions; local heights; Mordell-Weil groups; prime of good reduction

UR - http://eudml.org/doc/207242

ER -

## References

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- [2] Y. Ihara, On Fermat quotient and 'differentiation of numbers', RIMS Kokyuroku 810 (Algebraic Analysis and Number Theory) (1992), 324-341 (in Japanese). Zbl0966.11509
- [3] P. Ribenboim, Catalan's Conjecture, Academic Press, 1994. Zbl0824.11010
- [4] A. Schinzel, Primitive divisors of the expression ${A}^{n}-{B}^{n}$ in algebraic number fields, J. Reine Angew. Math. 268 (1974), 27-33. Zbl0287.12014
- [5] J. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
- [6] J. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. Zbl0729.14026
- [7] J. Silverman, Wieferich's criterion and the abc-conjecture, J. Number Theory 30 (1988), 226-237. Zbl0654.10019
- [8] K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892), 265-284.

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