“…That is, (q, k) is circular if and only if (p r ′ , k) is circular for some r ′ ∈ N such that k | (p r ′ − 1). Thus, we say that the pair (p, k) is circular if (p r ′ , k) is circular for some r ′ ∈ N. Now, the formula for the number of solutions of (1.1) given in [11] and [12] was actually under another constraint when k is odd. Namely, when k is odd, it was conveniently required that (p, 2k) is also circular.…”