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A Geometric Construction Involving Wilson’s Theorem

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Kenneth J. Prevot
10.5120/ijca2017915463

Kenneth J Prevot. A Geometric Construction Involving Wilson’s Theorem. International Journal of Computer Applications 175(1):6-8, October 2017. BibTeX

@article{10.5120/ijca2017915463,
	author = {Kenneth J. Prevot},
	title = {A Geometric Construction Involving Wilson’s Theorem},
	journal = {International Journal of Computer Applications},
	issue_date = {October 2017},
	volume = {175},
	number = {1},
	month = {Oct},
	year = {2017},
	issn = {0975-8887},
	pages = {6-8},
	numpages = {3},
	url = {http://www.ijcaonline.org/archives/volume175/number1/28450-2017915463},
	doi = {10.5120/ijca2017915463},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

A long standing result in number theory is Wilson’s Theorem, which states that n is a prime number if and only if (n – 1)! ≡ (-1) mod n. One motivation for this study is to detect some algebraic congruence relations which naturally arise in this number theoretic context, strictly through geometric constructions. Some examples of such congruence relations are presented. Namely, than n is an odd prime if and only if (n – 2)! – n(n – 3)/2 ≡ 1 mod (n2 -2n). Also if n is an odd prime, one has (n – 2)((n – 1)!)+(n –1) ≡1 mod (n2 – 2n).

References

  1. Rosen, K. H., Elementary Number Theory and its applications, 4th edition, Addison Wesley Longman, Reading, Massachusetts, 1999.
  2. Gabai, David, “Foliations and topology of 3-manifolds,” J. Diff. Georm. 18 (1983) no. 3, 445-503.

Keywords

Chimney, Sleeve, Wilson’s Theorem, Geometric Construction