  A sequence in an additively written abelian group is called zero-free if each
of its nonempty subsequences has sum different from the zero element of the
group. The article determines the structure of the zero-free sequences with
lengths greater than $n/2$ in the additive group $\Zn/$ of integers modulo $n$.
The main result states that for each zero-free sequence $(a_i)_{i=1}^\ell$ of
length $\ell>n/2$ in $\Zn/$ there is an integer $g$ coprime to $n$ such that if
$\bar{ga_i}$ denotes the least positive integer in the congruence class $ga_i$
(modulo $n$), then $\Sigma_{i=1}^\ell\bar{ga_i}<n$. The answers to a number of
frequently asked zero-sum questions for cyclic groups follow as immediate
consequences. Among other applications, best possible lower bounds are
established for the maximum multiplicity of a term in a zero-free sequence with
length greater than $n/2$, as well as for the maximum multiplicity of a
generator. The approach is combinatorial and does not appeal to previously
known nontrivial facts.
