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Divisibility Tests: A History and User's Guide - References

Author(s): 
Eric L. McDowell (Berry College)

[1] Abodah Zarah. Babylonian Talmud, folio 9b. Soncino Press, 1961.

[2] G. B. Attwood and D. Yih. Divisibility rules. Mathematics in School, 11(2):25, 1982.

[3] Aaron Bakst. Mathematical recreations. The Mathematics Teacher, 46(1):55-57, 1953.

[4] Lewis Berenson. A divisibility test for amateur discoverers. The Arithmetic Teacher, 17(1):39-41, 1970.

[5] Edward Brooks. The Philosophy of Arithmetic. Normal Publishing Company, 1880.

[6] Yonah Cherniavsky and Artour Mouftakhov. Zbikowski's divisibility criterion. The College Mathematics Journal, 45(1):17-21, 2014.

[7] Paul Cohn. Note 1644: Tests for divisibility. The Mathematical Gazette, 27(273):28-29, 1943.

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[9] S. S. Dalal. Note 2983. A divisibility test. The Mathematical Gazette, 46(355):31-32, 1962.

[10] Leonard Eugene Dickson. History of the Theory of Numbers. Chelsea Publishing Company, 1952. (Originally published in 1919 by the Carnegie Institution, Washington, D.C., all three volumes of this text are now available in paperback from Dover Publications, Mineola, NY, 2005.)

[11] Clayton W. Dodge. Divisibility tests - making order out of chaos. Pi Mu Epsilon Journal, 10(10):779-790, 1999.

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[13] William Donnell. Discovering divisibility tests. Mathematics in School, 37(3):14-15, 2008.

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[16] Richard English. Tests for divisibility in all number bases. Mathematics in School, 14(2):6-7, 1985.

[17] Sandy Ganzell. Divisibility tests, old and new. The College Mathematics Journal, 48(1):36-40, 2017.

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[20] Wm. E. Heal. Some divisibility tests. The American Mathematical Monthly, 4(6/7):171-172, 1897.

[21] Harry Hutchins. License numbers and divisibility rules. The Two-Year College Mathematics Journal, 14(2):122-125, 1983.

[22] John Q. Jordan. Divisibility tests of the noncongruence type. The Mathematics Teacher, 58(8):709-712, 1965.

[23] J. Kashangaki. Note 80.3: A test for divisibility by seven. The Mathematical Gazette, 80(487):226, 1996.

[24] Robert E. Kennedy. Divisibility by integers ending in 1, 3, 7, or 9. The Mathematics Teacher, 64(2):137-138, 1971.

[25] Alma Jean Kilgour. Divisibility by odd numbers. The Arithmetic Teacher, 7(3):150-151, 1960.

[26] Robb T. Koether. A general test for divisibility. Pi Mu Epsilon Journal, 5(8):420-424, 1973.

[27] Joseph-Louis Lagrange. Leçons élémentaires sur les math. données á l'école normale en 1795. Journal de l'école polytechnique, 7,8:194-199, 1812.

[28] Calvin T. Long. A simpler "7" divisibility rule. The Mathematics Teacher, 64(5):473-475, 1971.

[29] Kenneth J. McCaffrey. Digital sum divisibility tests. The Mathematics Teacher, 69(8):670-674, 1976.

[30] M. E. Mortimer and F. H. C. Oates. Divisibility revisited. Mathematics in School, 14(2):8-9, 1985.

[31] R. L. Morton. Divisibility by 7, 11, 13, and greater primes. The Mathematics Teacher, 61(4):370-373, 1968.

[32] Fletcher R. Norris. 1001 properties. The Mathematics Teacher, 69(7):577-578, 1976.

[33] Charlene Oliver. Gus's magic numbers: A key to the divisibility test for primes. The Arithmetic Teacher, 19(3):183-189, 1972.

[34] Allen Olsen. Divisibility tests. The Mathematics Teacher, 100(1):46-52, 2006.

[35] S. Parameswaran. Note 1920: Tests for divisibility. The Mathematical Gazette, 30(290):164-165, 1946.

[36] A. R. Pargeter. Divisibility tests. Mathematics in School, 2(4):40, 1973.

[37] Blaise Pascal. Oeuvres complètes. Gallimard, 1954.

[38] Phil Plummer. Divisibility tests for primes greater than 5. Pi Mu Epsilon Journal, 10(2):96-98, 1995.

[39] Robert Pruitt. A general divisibility test. The Mathematics Teacher, 59(1):31-33, 1966.

[40] Don Redmond. Divisibility tests. The Mathematics Teacher, 102(2):87-89, 2008.

[41] Marc Renault. Stupid divisibility tricks: 101 ways to stupefy your friends. Math Horizons, 14(2):18-21, 42, November 2006.

[42] Kenneth A. Seymour. A general test for divisibility. The Mathematics Teacher, 56(3):151-154, 1963.

[43] Richard Singer. Modular arithmetic and divisibility criteria. The Mathematics Teacher, 63(8):653-656, 1970.

[44] Lehi T. Smith. A general test of divisibility. The Mathematics Teacher, 71(8):668-669, 1978.

[45] Walter Szetela. A general divisibility test for whole numbers. The Mathematics Teacher, 73(3):223-225, 1980.

[46] R. A. Watson. Note 87.54: Tests for divisibility. The Mathematical Gazette, 87(510):493-494, 2003.

[47] Jonathan Weitsman. A general test for divisibility by primes. The Mathematical Gazette, 64(430):255-262, 1980.

[48] Joseph Whittaker. A new divisibility algorithm. The College Mathematics Journal, 16(4):268-276, 1985.

[49] Wendell M. Williams. A complete set of elementary rules for testing for divisibility. The Mathematics Teacher, 56(6):437-442, 1963.

[50] Najib Yazbak. Some unusual tests of divisibility. The Mathematics Teacher, 69(8):667-668, 1976.

[51] A. Zbikowski. Note sur la divisibilité des nombres. Bull. Acad. Sci. St. Pétersbourg, 3:151-153, 1861.

Eric L. McDowell (Berry College), "Divisibility Tests: A History and User's Guide - References," Convergence (May 2018)

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