Prove this: $\mathbb Z[i]/(1+2i)\simeq\mathbb Z_5$

Question

$$\mathbb Z[i]/(1+2i)\simeq\mathbb Z_5$$

Help me with this.

This is not very fair @drhab. I wrote that and you didn't aprove my edit. — User2020201, Apr 01 '20 at 14:12
@User2020201 I didn't approve your edit because I was not aware of any edit. Btw, what does it matter? — drhab, Apr 01 '20 at 14:14
@User2020201 I will now and then look for answers that you give. If I find one that is okay then I will upvote. $10>2$. Deal? — drhab, Apr 01 '20 at 14:18

score 0 · Answer 1 · answered Apr 01 '20 at 14:15

0

Consider the homomorphism $$\phi:\Bbb Z[i]\rightarrow\Bbb Z_5\\a+bi\mapsto a^2+b^2$$

Show that:

answered Apr 01 '20 at 14:15

1 Answers1