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Lemma 4 ([Binary congruences]). Let z_1,…,z_r∈ℤ _2[G] . Given M≥1 , if b>r(2^M-1) , there is an x≠0 such that (z_j)_x≡(z_j)_02^M (1≤j≤r). The bound depends on the number of tests and their precision, and not on the group-ring coefficients.