On the solvability of x2 = b(Mod m)

Tommy Dreyfus; Theodore Eisenberg

doi:10.1080/0020739830140404

On the solvability of x² = b(Mod m)

Tommy Dreyfus, Theodore Eisenberg

Department of Mathematics

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

Abstract

Euler's criterion is the usual procedure used for assessing the solvability of the equation x² = b(mod m). This criterion is applicable only when b and m are relatively prime and must be applied to each b (0 ≤b < m). Described in this paper is an alternative criterion which characterizes and counts, for a general modulus m, all numbers b for which x² = b(mod m) is solvable.

Original language	English
Pages (from-to)	415-421
Number of pages	7
Journal	International Journal of Mathematical Education in Science and Technology
Volume	14
Issue number	4
DOIs	https://doi.org/10.1080/0020739830140404
State	Published - 1 Jan 1983

ASJC Scopus subject areas

Mathematics (miscellaneous)
Education
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1080/0020739830140404

Cite this

@article{2b60617be8494fc0928101c67b7eede6,

title = "On the solvability of x2 = b(Mod m)",

abstract = "Euler's criterion is the usual procedure used for assessing the solvability of the equation x2 = b(mod m). This criterion is applicable only when b and m are relatively prime and must be applied to each b (0 ≤b < m). Described in this paper is an alternative criterion which characterizes and counts, for a general modulus m, all numbers b for which x2 = b(mod m) is solvable.",

author = "Tommy Dreyfus and Theodore Eisenberg",

year = "1983",

month = jan,

day = "1",

doi = "10.1080/0020739830140404",

language = "English",

volume = "14",

pages = "415--421",

journal = "International Journal of Mathematical Education in Science and Technology",

issn = "0020-739X",

publisher = "Taylor and Francis Ltd.",

number = "4",

}

TY - JOUR

T1 - On the solvability of x2 = b(Mod m)

AU - Dreyfus, Tommy

AU - Eisenberg, Theodore

PY - 1983/1/1

Y1 - 1983/1/1

N2 - Euler's criterion is the usual procedure used for assessing the solvability of the equation x2 = b(mod m). This criterion is applicable only when b and m are relatively prime and must be applied to each b (0 ≤b < m). Described in this paper is an alternative criterion which characterizes and counts, for a general modulus m, all numbers b for which x2 = b(mod m) is solvable.

AB - Euler's criterion is the usual procedure used for assessing the solvability of the equation x2 = b(mod m). This criterion is applicable only when b and m are relatively prime and must be applied to each b (0 ≤b < m). Described in this paper is an alternative criterion which characterizes and counts, for a general modulus m, all numbers b for which x2 = b(mod m) is solvable.

UR - http://www.scopus.com/inward/record.url?scp=84946653459&partnerID=8YFLogxK

U2 - 10.1080/0020739830140404

DO - 10.1080/0020739830140404

M3 - Article

AN - SCOPUS:84946653459

SN - 0020-739X

VL - 14

SP - 415

EP - 421

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

IS - 4

ER -