Coloring so that no Pythagorean Triple is Monochromatic
نویسندگان
چکیده
We address the question of the “partition regularity” of the Pythagorean equation a+b = c; in particular, can the natural numbers be assigned a 2-coloring, so that no Pythagorean triple (i.e., a solution to the equation) is monochromatic? We prove that the hypergraph of Pythagorean triples can contain no Steiner triple systems, a natural obstruction to 2-colorability. Then, after transforming the question into one about 3-CNF satisfiability and applying some reductions, a SAT solver is used to find a 2-coloring for {1, . . . , 7664}. Work continues as we seek to improve the reductions and extend the computation.
منابع مشابه
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ورودعنوان ژورنال:
- CoRR
دوره abs/1505.02222 شماره
صفحات -
تاریخ انتشار 2015