Monochromatic Homothetic Copies of F1ò 1 + Sò 1 + S + Tg

@inproceedings{Brown1997MonochromaticHC,
  title={Monochromatic Homothetic Copies of F1{\`o} 1 + S{\`o} 1 + S + Tg},
  author={Tom C. Brown and Bruce M. Landman and Marni Mishna},
  year={1997}
}
For positive integers s and t, let f (sÒ t) denote the smallest positive integer N such that every 2-colouring of [1ÒN] = f1Ò 2Ò    ÒNg has a monochromatic homothetic copy of f1Ò 1 + sÒ 1 + s + tg. We show that f (sÒ t) = 4(s + t) + 1 whenever sÛg and tÛg are not congruent to 0 (modulo 4), where g = gcd(sÒ t). This can be viewed as a generalization of… CONTINUE READING