Let ��,� and ��,� be the functions defined in Schroder's method of the first and second kind for an entire function f with given order n (�>= 2), respectively. Based on unrefined algebra characterizations of ��,� and ��,�, we obtain some sufficient conditions on f such that both ��,� and ��,� possess given finite pairs of extraneous non-repelling cycles. Here, these conditions are a pair of equations, which have infinitely many polynomials or transcendental entire functions as its solutions. For obtaining some solutions f of ...
