Bibliographic Details
| Title: |
Pascal's Triangle Modulo 3. |
| Authors: |
WILSON, AVERY1 |
| Source: |
Mathematical Spectrum. 2014/2015, Vol. 47 Issue 2, p72-75. 4p. |
| Subjects: |
Pascal's triangle, Binomial coefficients, Fractals, Moduli theory, Coefficients (Statistics) |
| Abstract: |
If you colour the odd entries of Pascal's triangle red and the even entries blue, a beautiful fractal pattern known as Sierpinski's gasket appears. A well-known problem is to determine how many odd entries appear in any given row of Pascal's triangle. A natural generalization of this problem is to ask, if we look at the nth row of Pascal's triangle modulo any positive integer m, how many occurrences of each residue c lass 0, 1, 2,..., m-1 will we find? Patterns are hard to come by for composite moduli, but nice formulae can be found for prime moduli. In this article, I derive the solution for the modulo 3 case of the problem using Lucas' theorem on binomial coefficients modulo a prime. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
