Monochromatic and Zero-Sum Sets of Nondecreasing Modified Diameter

Let $m$ be a positive integer whose smallest prime divisor is denoted by $p$, and let ${\Bbb Z}_m$ denote the cyclic group of residues modulo $m$. For a set $B=\{x_1,x_2,\ldots,x_m\}$ of $m$ integers satisfying $x_1

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