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Jun 8, 2015 at 18:24 comment added Joel Moreira Yes, that's the easy argument I had in mind. I suspected this might be open (as many other corollaries of Chowla's conjecture)... Thanks for the references on the progress so far. I am intrigued by the result you mentioned about progressions with arbitrary sign patterns, I don't see how it follows from Mobius orthogonality plus the inverse Gowers norm conjecture. I am also wondering if it comes with statistics about the "proportion" of progressions with a given sign pattern.
Jun 8, 2015 at 5:09 vote accept Joel Moreira
Jun 7, 2015 at 21:27 history edited Terry Tao CC BY-SA 3.0
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Jun 7, 2015 at 21:15 history edited Terry Tao CC BY-SA 3.0
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Jun 7, 2015 at 21:06 history answered Terry Tao CC BY-SA 3.0