Snevily's conjecture it is an open conjecture in Group theory for non cyclic Group and it were proved for abelian groups of prime order using a fairly standard application of the Alon-Tarsi polynomial technique .It states that:
Snevily's conjecture: let $G$ be an abelian Group of odd order and let $A,B \subseteq G$ satisfy $|A|=|B|=k$ .Then the elements of $A$ and $B$ may be ordered $A=\{a_1\cdots a_k\}$ and $B=\{b_1\cdots b_k\}$ so that the sums $a_1+b_1,a_2+b_2,\cdots a_k+b_k$ are pairwise distinct .
its seems that conjecture has connection to analytic number theory such that , This conjecture were proved for $\mathbb{Z_n}$ a subgroup of the multiplicative group of the field of order $2^{\phi(n)}$ with $\phi(n)$ is the Euler totiont function , Now my question here is : What are the consequence of Snevily's conjecture to analytic number theory if really there is a connection between them?
Addedendum :I have added this paper entitled "Divisors of the number of Latin rectangles" just to show the connection between latine square which it is the source of the titled conjecture and number divisors (number theory) .This means probably we will have some consequence of the titled conjecture to analytic number theory in the futur.
