TL;DR
This paper investigates modular Schur numbers related to systems of linear equations, revealing their dependence solely on the number of equations and establishing stronger bounds for single-equation cases.
Contribution
It demonstrates that modular Schur numbers depend only on the number of equations and provides improved bounds for the single-equation scenario.
Findings
Modular Schur numbers depend only on the number of equations.
Stronger bounds are established for the case of one equation.
Dependence on coefficients is eliminated in the modular setting.
Abstract
We study modular analogues of Schur numbers for systems of linear equations. We show that these only depend on the number of equations, not their coefficients and in the case of one equation show stronger bounds.
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