On the elliptic curves modulo p

Daeyeoul Kim; Ja Kyung Koo; Yoon Kyung Park

doi:10.1016/j.jnt.2007.04.015

On the elliptic curves modulo p

Daeyeoul Kim
, Ja Kyung Koo
, Yoon Kyung Park

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We first prove Sun's three conjectures [Z.H. Sun, On the number of incongruent residues of x⁴ + a x² + b x modulo p, J. Number Theory 119 (2006) 210-241; Z.H. Sun, http://sfb.hytc.edu.cn/xsjl/szh/, 2000, June] on the number of rational points of some elliptic curves over finite fields F_p, which are related to the congruence cubic and quartic residue. And we provide some examples and comments concerning these conjectures.

Original language	English
Pages (from-to)	945-953
Number of pages	9
Journal	Journal of Number Theory
Volume	128
Issue number	4
DOIs	https://doi.org/10.1016/j.jnt.2007.04.015
State	Published - Apr 2008

Keywords

Elliptic curves

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10.1016/j.jnt.2007.04.015

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title = "On the elliptic curves modulo p",

abstract = "We first prove Sun's three conjectures [Z.H. Sun, On the number of incongruent residues of x4 + a x2 + b x modulo p, J. Number Theory 119 (2006) 210-241; Z.H. Sun, http://sfb.hytc.edu.cn/xsjl/szh/, 2000, June] on the number of rational points of some elliptic curves over finite fields Fp, which are related to the congruence cubic and quartic residue. And we provide some examples and comments concerning these conjectures.",

keywords = "Elliptic curves",

author = "Daeyeoul Kim and Koo, \{Ja Kyung\} and Park, \{Yoon Kyung\}",

year = "2008",

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doi = "10.1016/j.jnt.2007.04.015",

language = "English",

volume = "128",

pages = "945--953",

journal = "Journal of Number Theory",

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AU - Kim, Daeyeoul

AU - Koo, Ja Kyung

AU - Park, Yoon Kyung

PY - 2008/4

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N2 - We first prove Sun's three conjectures [Z.H. Sun, On the number of incongruent residues of x4 + a x2 + b x modulo p, J. Number Theory 119 (2006) 210-241; Z.H. Sun, http://sfb.hytc.edu.cn/xsjl/szh/, 2000, June] on the number of rational points of some elliptic curves over finite fields Fp, which are related to the congruence cubic and quartic residue. And we provide some examples and comments concerning these conjectures.

AB - We first prove Sun's three conjectures [Z.H. Sun, On the number of incongruent residues of x4 + a x2 + b x modulo p, J. Number Theory 119 (2006) 210-241; Z.H. Sun, http://sfb.hytc.edu.cn/xsjl/szh/, 2000, June] on the number of rational points of some elliptic curves over finite fields Fp, which are related to the congruence cubic and quartic residue. And we provide some examples and comments concerning these conjectures.

KW - Elliptic curves

UR - https://www.scopus.com/pages/publications/39749120845

U2 - 10.1016/j.jnt.2007.04.015

DO - 10.1016/j.jnt.2007.04.015

M3 - Article

AN - SCOPUS:39749120845

SN - 0022-314X

VL - 128

SP - 945

EP - 953

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 4

ER -

On the elliptic curves modulo p

Abstract

Keywords

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