Two square weighted zero-sum constants

Santanu Mondal, Krishnendu Paul, Shameek Paul

Published 2022-02-26Version 1

The constant $D_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $\mathbb Z_n$ has a subsequence whose $A$-weighted sum is zero. i.e., some linear combination of its terms is zero, where the coefficients are taken from the set $A$. We determine the value of $D_A(n)$ and also the value of a related constant $C_A(n)$, when $A$ is the set of all non-zero squares in $\mathbb Z_n$.