  A tight Heffter array H(m,n) is an m x n matrix with nonzero entries from
Z_{2mn+1} such that i) the sum of the elements in each row and each column is
0, and ii) no element from {x,-x\ appears twice. We prove that H(m,n) exist if
and only if both m and n are at least 3. If all entries are integers of
magnitude at most mn satisfying every row and column sum is 0 over the integers
and also satisfying ii) we call H an integer Heffter array. We show integer
Heffter arrays exist if and only if mn \equiv 0,3 (mod 4). Finally, an integer
Heffter array is shiftable if each row and column contains an the same number
of positive and negative integers. We show that shiftable integer arrays exists
exactly when both $m,n$ are even.
  This research report contains all of the details of the proofs. It is meant
to accompany the journal version of this paper.
