For two distinct integers m1, m2 ≥ 2, we set α1 = [0; 1, m1] and α2 = [0; 1, m2] (where [0; 1, m] is the continued fraction [0; 1, m, 1, m, 1, m, . . .]) and we let S_α1 (n) and S_α2(n) denote respectively, the sum of digits functions in the Ostrowski α1 and α2−representations of n. Let b1, b2 be positive integers satisfying (b1, m1) = 1 and (b2, m2) = 1, we obtain an estimation N/b1b2 with an error term O(N1−δ) for the cardinality of the following set { n, 0 ≤ n < N; S_α1(n) ≡ a1 (mod b1), S_α2(n) ≡ a2 (mod b2)} for all integers a1 and a2. Our result should be compared to that of Bésineau and Kim who addressed the case of the q−representations in different bases (that are coprime).