Is division in Eisenstein integers unique?

Viewed 12

Given x & y in Z[ω], the set of Eisenstein integers, how many q & r are there in Z[ω], such that x = q * y + r, where N(r) < N(y).

For example,

14 + 60ω = (10+3ω)(3 + 7ω) + (5+2ω) = (10 + 2ω)(3+7ω)+ (-2-2ω).

0 Answers
Related