M*A*T*H Colloquium

Anisah Nu'man from Spelman College will present: Rainbow Numbers for x + ky = z. An exact r-coloring of a set S is a surjective function c:S → {1, 2,…,r}. The rainbow number of a set S (for example, {10, 20, 30, 40}) for an equation (such as x1 + x2 = x3) is the smallest integer r such that every exact r-coloring of the set S contains a “rainbow solution:” a solution to the equation in which all values are assigned different colors (so in our example, either {10, 20, 30} or {10, 30, 40} would have to be mapped to three different colors). We will explore upper and lower bounds for the rainbow number of the set {1, 2,…,n} for the equation x + ky = z, where k is a positive integer.

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