The generalised weak Schur number, denoted by WS(k, l), is defined to be the largest positive integer n such that the set \([n]=\{1,2,\dots ,n\}\) can be partitioned into k disjoint subsets that do not contain solutions to the equation \(x_1+\dots +x_l=y\) where the numbers \(x_1,\dots ,x_l,y\) are pairwise distinct. The generalised weak Schur number modulo m, denoted by \(WS_m(k,l)\) , is similarly defined with equality swapped for congruence modulo m. In 2023, Ahmed, Boza, Revuelta, and Sanz found new exact values and lowers bounds for WS(k, l). However, since 2013, the values of \(WS_m(k,l)\) are only known for \(m=1,2,3\) . In this paper, we determine new exact values and bounds for \(WS_m(k,l)\) for general values of m. In particular, we establish that \(kl \le WS_m(k,l) \le klm-1\) and found the exact value of \(WS_m(1,l)\) when l is large enough. Furthermore, when m is a prime and \(l\not \equiv 1\pmod m\) , we also determine the exact values of \(WS_m(k,l)\) under the conditions that l and k are large.
