Finally let's look at Pascal's triangle in mod 7. Here, every entry is divided by 7 to produce remainders of 0, 1, 2, 3, 4, 5 or 6. Below is again the first ten rows of Pascal's triangle in mod 7.
By assigning different colors to each remainder, we can see that there is fewer numbers with the remainder of 0 than before! Light blue has been added to represent the remainder of 5 and gray represents 6.
This time we only need to expand our entries to the 48th row to see the complete pattern. We can see that now the white space represents values that are multiples of 7, and there seems to be less white space than in the other mod patterns. Again the smaller triangle in the upper left corner is repeated at a larger and larger scale throughout the entire triangle. Notice how this pattern occurs regardless of the size of the triangles. What do you think the pattern would look like if we were to expand our entries even further? Other than the triangle color pattern, what other patterns do you notice within each smaller triangle?
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