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Monochromatic Sums Equal to Products in ℕ
Published/Copyright:
August 4, 2011
Abstract
Csikvári, Gyarmati, and Sárközy asked whether, whenever the set ℕ of positive integers is finitely colored, there must exist monochromatic a, b, c, and d with a ≠ b such that a + b = cd. We provide an affirmative answer, showing that a much stronger statement is true.
Received: 2009-11-05
Accepted: 2009-11-24
Published Online: 2011-08-04
Published in Print: 2011-August
© de Gruyter 2011
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Articles in the same Issue
- The Number of Solutions of λ(x) = n
- Monochromatic Sums Equal to Products in ℕ
- On the Sum of Reciprocal Generalized Fibonacci Numbers
- Recursively Self-Conjugate Partitions
- Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
- Algebraic Proof for the Geometric Structure of Sumsets
- An Erdős–Fuchs Type Theorem for Finite Groups
- Coincidences of Catalan and q-Catalan Numbers
- Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
- Perfect Numbers with Identical Digits
- Remarks on the Pólya–Vinogradov Inequality
- Heights of Divisors of xn – 1
- Bernoulli Numbers and Generalized Factorial Sums
- Witten Volume Formulas for Semi-Simple Lie Algebras
