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Using the notion of the composita, we obtain a method of solving iterativefunctional equations of the form $A^{2^n}(x)=F(x)$, where $F(x)=\sum_{n>0}f(n)x^n$, $f(1)\neq 0$. We prove that if $F(x)=\sum_{n>0} f(n)x^n$ has integercoefficients, then the generating function $A(x)=\sum_{n>0}a(n)x^n$, which isobtained from the iterative functional equation $4A(A(x))=F(4x)$, has integercoefficients.  Key words: iterative functional equation, composition of generatingfunctions, composita.

Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$