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 (Formula presented.) whenever the necessary conditions hold, that is, (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.). By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever (Formula presented.) is odd and (Formula presented.).