Toward a Solution of Archdeacon's Conjecture on Integer Heffter Arrays

In this article, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays H(m, n; s, k) whenever the necessary conditions hold, that is, 3 ⩽ s ⩽n, 3 ⩽ k ⩽m, ms = nk and nk ≡ 0, 3 (mod 4). By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever k ⩾ s gcd( s, k ) is odd and s ≠ 3, 5, 6, 10.