Non-canonical Extensions of Erdős-Ginzburg-Ziv Theorem
Ravindranathan Thangadurai · Zenodo (CERN European Organization for Nuclear Research) · 2002
In 1961, Erdös-Ginzburg-Ziv proved that for a given natural number n ≥ 1 and a sequence a1, a2, ··· , a2n−1 of integers (not necessarily distinct), there exist 1 ≤ i1 < i2 < ··· < in ≤ 2n − 1 such that ai1 + ai2 + ··· + ain is divisible by n. Moreover, the constant 2n − 1 is tight. By now, there are many canonical generalizations of this theorem. In this paper, we shall prove some non-canonical generalizations of this theorem.