ABSTRACT
Let represent the equation x1 + x2 + ⋅⋅⋅ + xt − 1 = xt. For k ≥ 1, 0 ≤ i ≤ k − 1, and ti ≥ 3, the generalized Schur number S(k; t0, t1, …, tk − 1) is the least positive integer m such that for every k-coloring of {1, 2, …, m}, there exists an i ∈ {0, 1, …, k − 1} such that there exists a solution to
that is monochromatic in color i. In this article, we report 26 previously unknown values of S(k; t0, t1, …, tk − 1) and conjecture that for 4 ≤ t0 ≤ t1 ≤ t2, S(3; t0, t1, t2) = t2t1t0 − t2t1 − t2 − 1.
Acknowledgments
The authors would like to thank the referee for his/her helpful comments and suggestions for improving the presentation of the paper. The first author would like to thank Professor Clement Lam for his support.