Pascal's Triangle and Its Relatives

Exercises

Other mods

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

0 (mod 6)	1, 2, 3, 4, or 5 (mod 6)	1, 3, or 5 (mod 6)	1, 2, 4, or 5 (mod 6)

First note H1 = {0,2,4} is a subgroup isomorphic to Z3, so Z6/H1 is isomorphic to Z2 and the coset 1 + H1 corresponds to 1 in Z2. This explains the third picture.

Next note H2 = {0,3} is a subgroup isomorphic to Z2, so Z6/H2 is isomorphic to Z3 and the cosets 1 + H2 and 2 + H2 correspond to 1 and 2 in Z3. This explains the fourth picture.

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