I can probably work out part ii). if I can do part i).Is there a complete set of residues modulo p consisting of perfect squares:

i). When p=7.

ii). for any prime p.

I think part i) is true but I can't figure out the set. My set so far is $\displaystyle \{0,36,9\}$ for 0,1 and 2 respectively and $\displaystyle \{25 \}$ for 4.

I can't find any perfect squares for 3,5 and 6!