Is the half-filled magic square problem NP-complete? Here is the problem:

We have a square with some numbers from 1..N in some cells. It's needed to determine if it can be completed to a magic square.

Examples:

2 _ 6       2 7 6
_ 5 1  &gt;&gt;&gt;  9 5 1
4 3 _       4 3 8

7 _ _ 
9 _ _  &gt;&gt;&gt;  NO SOLUTION 
8 _ _


Is this problem NP-complete? If yes, how can I prove it?

Crosspost on MS
Filling a partially-filled Latin square is NP-Complete. "The complexity of completing partial Latin squares" Charles J. Colbourn. Discrete Applied Mathematics, Volume 8, Issue 1, April 1984, Pages 25-30 http://dx.doi.org/10.1016/0166-218X(84)90075-1

Can a Latin square problem be turned into a magic square problem via modular arithmetic? My intuition says yes, but the rest of my brain says "Get back to grading!"