منابع مشابه
Multiplicity of monochromatic solutions to x+yz
For integers n ≥ 1 and k ≥ 0, let Mk (n) represent the minimum number of monochromatic solutions to x + y < z over all 2-colorings of {k + 1, k + 2, . . . , k + n} . We show that for any k ≥ 0, Mk (n) = Cn3(1 + ok(1)), where C = 1 12(1+22)2 ≈ .005686. A structural result is also proven, which can be used to determine the exact value of Mk(n) for given k and n.
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2019
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2017-036-1