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Let   a   and   r   be positive integers. By definition,s    aris the least positive integer such that, for any   r  -coloring of the interval1  ,    s    ar, there exists a monochromatic solution to   x  +  a  y  =  z  . For   a  =  1  , the numbers   s    r    =    s    1rare classical Schur numbers. In this paper, we study the numberss    arfor   a  ≥  2  .

journal of mathematics

On Generalized Schur Numbers of the Equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:math>

On Generalized Schur Numbers of the Equation x+ay=z