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Assuming the Generalised Riemann Hypothesis for Dirichlet $L$-functions (GRH), we show that for every sufficiently large even integer $N$ there are $a,b \\geq 1$ such that $$ a+b = N \\text{ and } \\lambda(a) = \\lambda(b) = -1. $$ This conditionally answers an analogue of the binary Goldbach problem for the Liouville function, posed by Shusterman.\n  The latter is a consequence of a quantitative lower bound on the frequency of sign patterns attained by $(\\lambda(n),\\lambda(N-n))$, for sufficiently large primes $N$. 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