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Italian mathematician Girolamo Cardano published the solutions to the cubic Abstract algebra was developed in the 19th century, deriving from the interest in solving. 7th + Student Solutions Manual 7th Edition 1834 Problems solved: Joseph A. Gallian: Student Solutions Manual for Gallian's Contemporary Abstract Algebra 7th Edition 1834 Problems solved: Joseph A. Gallian: Introduction to Advanced Since e is one solution it suffices to show that nonidentity solutions come in distinct pairs. To this end note that if x3 = e and x = e, then (x−1 )3 = e and x = x−1. So if we can find one nonidentity solution we can find a second one. Now suppose that a and a−1 are nonidentity elements that satisfy x3 = e. Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th � Gallian, Joseph � Other Popular Editions of the Same Title � Customers who bought this�. 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