Pascal's Triangle and Its Relatives

Exercises

Other mods

1. (mod 4) Shading the boxes of Pascal's triangle with numbers congruent to

0 (mod 4)	1 (mod 4)	2 (mod 4)	3 (mod 4)

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

Note that H = {0, 2} is a subgroup of Z4 and that H is ispmorphic to Z2.

Under the isomorphism Z4/H -> Z2, the coset 1 + H = {1,3} corresponds to 1 in Z2 and the coset 0 + H = {0,2} corresponds to 0 in Z2.

Note that 1 + H in Z4 has the same Pascal's triangle as 1 in Z2.

Return to Other Mod Exercises.