Question 145
The $1,2, \ldots, n$ numbers of two colors are colored, blue and red. Prove that if $n=2017$ there is such a coloration that the equation $$
8(x+y)=z
$$ has no monochromatic solutions. Determine the smallest $n$ for which it is never possible to color the numbers so that there are no monochromatic solutions.
8(x+y)=z
$$ has no monochromatic solutions. Determine the smallest $n$ for which it is never possible to color the numbers so that there are no monochromatic solutions.