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Monograph "B. Grechuk, Polynomial Diophantine equations. A systematic approach" suggests solving Diophantine equations systematically in certain order. Many hundreds of the equations are left to the reader. Here, we provide complete solutions to all these equations. The difficulties of solved equations range from elementary to research level. In the last section, we present a summary table of all solved equations ordered by their size, which makes them easy to find. As a result, this document may be used as a database of solved Diophantine equations of small size, to which more difficult equations can be reduced.
Ashleigh G. Wilcox (Fri,) studied this question.