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Carryless Arithmetic Mod 10

by David Applegate, Marc LeBrun, and Neil J. A. Sloane

Year of Award: 2013

Award: George Pólya

Publication Information: The College Mathematics Journal, Vol. 43, no. 1, January 2012, pp. 43-50.

Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet) Carryless arithmetic consists of adding and multiplying numbers with no carries into other digit positions. The authors' results can easily be used in a first course on number theory or abstract algebra.

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About the Author: (From the MathFest 2013 Prizes and Awards Booklet)

David Applegate received his Ph.D. in Computer Science from Carnegie Mellon, and has been at AT&T Shannon Labs since 2000. His research interests include combinatorial optimization, the Traveling Salesman Problem, and other mathematical diversions.

Marc LeBrun was confirmed as an ardent amateur mathematician at age ten, when Martin Gardner graciously answered his fan letter. He is delighted to find professional colleagues who share his interests in recreational arithmetic, and is an enthusiastic contributor to the On-Line Encyclopedia of Integer Sequences.

Neil J. A. Sloane was at AT&T Bell Labs and later AT&T Shannon Labs from 1969 to 2012. He has written many books and articles on mathematics, engineering and statistics. He also runs the On-Line Encyclopedia of Integer Sequences.

Subject classification(s): Algebra and Number Theory | Modular Arithmetic | Number Theory
Publication Date: 
Thursday, August 22, 2013