Ways of characterizing the dependence of one random variable on another (or several others) are investigated. In particular, an index of dependence of X on Y is introduced which (i) always eXists, (ii) lies between zero and unity inclusive, (iii) is zero if and only if X and Yare independent, (iv) is unity if X is a function of Y (and only if whenever X has finite variance), (v) may assume ever...

The index conjecture in zero-sum theory states that if gcd?(n,6)=1 then every minimal sequence of length 4 modulo n has 1. In this paper, we prove a version for all n>N some absolute constant N.