Abstract
For integers k, n with k,n≥1, the n-color weak Schur numberWSk(n) is defined as the least integer N, such that for every n-coloring of the integer interval [1, N], there exists a monochromatic solution x1,…,xk,xk+1 in that interval to the equation x1+x2+…+xk=xk+1, with xi≠xj, when i≠j. We show a relationship between WSk(n+1) and WSk(n) and a general lower bound on the WSk(n) is obtained.
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