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Let    $$A\subset \mathbb {N}_{+}$$  A ⊂ N + and by    $$P_{A}(n)$$  P A ( n ) denotes the number of partitions of an integer  n  into parts from the set  A . The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations of the form    $$P_{A}(x)=P_{B}(y)$$  P A ( x ) = P B ( y ) , where  A ,  B  are certain finite sets.

Equal values of certain partition functions via Diophantine equations