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- W2037202555 abstract "For relatively prime positive integers a and b, let $${n = mathcal{R}(a, b)}$$ denote the least positive integer such that every 2-colouring of [1, n] admits a monochromatic solution to ax + by = (a + b)z with x, y, z distinct integers. It is known that $${mathcal{R}(a, b) leq 4(a + b) + 1}$$ . We show that $${mathcal{R}(a, b) = 4(a + b) + 1}$$ , except when (a, b) = (3, 4) or (a, b) = (1, 4k) for some $${k geq 1}$$ , and $${mathcal{R}(a, b) = 4(a + b)-1}$$ in these exceptional cases." @default.
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- W2037202555 date "2015-04-29" @default.
- W2037202555 modified "2023-10-06" @default.
- W2037202555 title "The Two-Colour Rado Number for the Equation ax + by = (a + b)z" @default.
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- W2037202555 doi "https://doi.org/10.1007/s00026-015-0269-6" @default.
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