AHMED , T.

In this study, we focus on the concept of the 2-color off-diagonal generalized weak Schur numbers, denoted as WS(2; k1, k2). These numbers are defined for integers ki ≥ 2, where i = 1, 2, as the smallest integer M, such that any 2-coloring of the integer interval [1, M] must contain a 2-colored solution to the equation Ekj: x1 + x2 + ... + xkj...

For integers k, n with k, n ≥ 1, the n-color weak Schur number WSk (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 = x j , when i = j. In this paper, we obtain the exact...