The configuration x, y, x+y, y/x is partition regular in the naturals in a strong infinitary sense extending Hindman's theorem, while related product configurations of degree-one polynomials reduce to a few special cases.
Goswami,Monochromatic Translated Product and Answering Sahasrabudhe’s Conjecture
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The paper establishes existence of multiple rich monochromatic configurations in natural numbers via algebraic properties of sums of two squares in the Stone-Čech compactification βN.
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Monochromatic sums and quotients in $\mathbb N$
The configuration x, y, x+y, y/x is partition regular in the naturals in a strong infinitary sense extending Hindman's theorem, while related product configurations of degree-one polynomials reduce to a few special cases.
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Some monochromatic patterns in natural numbers
The paper establishes existence of multiple rich monochromatic configurations in natural numbers via algebraic properties of sums of two squares in the Stone-Čech compactification βN.