ERDŐS PROBLEM
18 / 21
P(ε)
Coloring the Integers to Avoid Monochromatic Sums
If the positive integers are finitely colored, must there exist x, y (not necessarily distinct) with x, y, x+y all the same color?
PRIZE
None specified
This is Schur's theorem (1916), a precursor to much of Erdős's later Ramsey-theoretic work on arithmetic structure in colorings.
Paul Erdős (1913–1996) · >1,500 papers · rotates daily