Abstract Algebra - ideals and generators

[TheColorCute]

Homework Statement

a.) Let a=3-8i and b=2+3i. Find x,y ϵ Z[i] such that ax+by=1.
b.) Show explicitly that the ideal I=(85,1+13i) $\subseteq$ Z[i] is principle by exhibiting a generator.

Homework Equations

Given ideal: I=(85,1+13i) $\subseteq$ Z[i]
a=3-8i
b=2+3i

Honestly, I am beyond lost on this problem. Any help would be appreciated. Thanks!

 

[micromass]

You should apply the division algorithm in a suitable way.