Pascal's Triangle and Its Relatives

Exercises

Other mods

6. (mod 9) Shading the boxes of Pascal's triangle with numbers congruent to

0 (mod 9)	1, ... 7, or 8 (mod 9)	1, 2, 4, 5, 7, or 8 (mod 9)

Observe Z9 has one proper subgroup,

H = {0,3,6}, ispmorphic to Z3.

Then Z9/H is isomorphic to Z3 and the union of cosets 1 + H and 2 + H, corresponds to {1,2} in Z3. This explains the third picture.

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