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In this paper, we refine the method introduced by Izadi and Baghalaghdam tosearch integer solutions to the Diophantine equation$X_1^5+X_2^5+X_3^5=Y_1^3+Y_2^3+Y_3^3$. We show that the Diophantine equationhas infinitely many positive solutions.

Remark on a Paper by Izadi and Baghalaghdam about Cubes and Fifth Powers Sums