Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers
Abstract
In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N2 satisfy the sets lambda x, lambda y, x y, lambda(x+y) and u+rho, v+rho, u v+rho, u+v being monochromatic. Using related arguments we also give two different proofs of a special case of the Milliken--Taylor theorem.
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