Question regarding quadraticlike residues in (Z/pZ)[i].
Hi all.
I'm working in the set that is formed by extending the integers mod p (p is prime and equal to 3 mod 4) by including i = [itex]\sqrt{1}[/itex]: (Z/pZ)[i]. I want to know if the exists a 'z' in (Z/pZ)[i] for a given nonzero element 'a' of Z/pZ such that 'a = z[itex]\overline{z}[/itex]'. If anyone could point me in a fruitful direction on this I would be most grateful. Z 
Re: Question regarding quadraticlike residues in (Z/pZ)[i].
You're basically asking if a is the sum of two squares in Z/pZ. This is true even if p != 3 mod 4. Try to mimic the proof of the fact that a prime = 1 mod 4 is the sum of two squares in Z.
For related material, you can try reading up on "formally real fields". (Z/pZ is a nonexample.) 
Re: Question regarding quadraticlike residues in (Z/pZ)[i].
Many thanks!

All times are GMT 5. The time now is 10:45 AM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums