The Two-Colour Rado Number for the Equation ax + by = (a + b)z
For relatively prime positive integers a and b, let n = 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 R(a,b) ≤ 4(a+b) +1. We show that R(a,b) = 4(a+b) +1, except wh...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer Basel,
2016-06-23T17:07:46Z.
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| Subjects: | |
| Online Access: | Get fulltext |