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title
I Can't Believe It's Not Random!
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Joel Moreira's math blog
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I Can't Believe It's Not Random!
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2026-03-03 10:57:53
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I Can't Believe It's Not Random! | Joel Moreira's math blog I Can't Believe It's Not Random! Joel Moreira's math blog Skip to content Home About ← Older posts Partition regularity of (generalized) Pythagorean pairs Posted on 12/07/2024 by Joel Moreira Nikos Frantzikinakis , Oleksiy Klurman and I have just uploaded to the arXiv our article entitled “Partition regularity of generalized Pythagorean pairs” which is a sequel to our previous paper “Partition regularity of Pythagorean pairs” . Both papers address the question of partition regularity of quadratic equations. A diophantine equation is partition regular if for every partition (or coloring) of the natural numbers into finitely many sets , some contains a solution to the equation. For linear equations partition regularity is characterized by Rado’s theorem , which I discussed in this previous blog post . According to Rado’s theorem, the linear equation is partition regular if and only if ...
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