# Group ring generated by Z and the quaternion group

I would like to calculate general $n$th power of $i+j$ in the group ring.

My idea was to find some patterns after calculating some powers of i+j, conjecture the general form of nth power of it and prove it by induction. But i cannot find any patterns...... So any help will be very appreciated.

• How many powers did you compute? – Tobias Kildetoft May 5 '16 at 11:24
• Quaternion group (not "quarternion group"). – Dietrich Burde May 5 '16 at 15:17
• It would help a lot if you show already calculated powers. – lisyarus May 24 '16 at 10:25