ON THE DISJUNCTIVE RADO NUMBER OF THE EQUATIONS ax1 = x2 AND bx1 + x2 = x3

Purcilly, Adam

Peacock Scholarship

ON THE DISJUNCTIVE RADO NUMBER OF THE EQUATIONS ax1 = x2 AND bx1 + x2 = x3

Public Deposited

For a given system of linear equations L, the Rado number of the system is the least integer n for which every t-coloring of {1,...,n} contains a monochromatic solution of one of the equations in L, if such an integer exists. In this thesis, the 2-color disjunctive Rado numbers for the equations ax1 = x2 and bx1 + x2 = x3 are determined for more than half of all values of a and b.

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