Under GRH, every sufficiently large even N has a+b=N with lambda(a)=lambda(b)=-1, and for prime N each of the four sign patterns occurs many times.
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On Shusterman's Goldbach-type problem for sign patterns of the Liouville function
Under GRH, every sufficiently large even N has a+b=N with lambda(a)=lambda(b)=-1, and for prime N each of the four sign patterns occurs many times.