A general lower bound on the weak Schur number

Description

For integers k, n with k, n ≥ 1, the n-color weak Schur number W Sk(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 6= xj , when i 6= j. We show a relationship between W Sk(n + 1) and W Sk(n) and a general lower bound on the W Sk(n) is obtained.

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