Copy of Patterns in Pascal’s Triangle Modulo m

This applet looks at patterns in the Pascal triangle based on the divisibility of the binomial coefficients. If we represent the entries in Pascal’s triangle as points, and color the odd and the even numbers in different colors, we will notice the fractal pattern of the Sierpinski triangle. The applet below is a generalization of this idea. Instead of looking only in divisibility by two, we can explore the patterns of divisibility of the binomial coefficients by any number . Another interesting question is to look for patterns in the distribution of the binomial coefficients based on the possible remainders (the residue classes).
  • To display one residue class, enter a number between and on the place of in the input box.
  • To display simultaneously several consecutive residue classes, click on the green arrow.