Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Catalan's conjecture is a theorem in number theory that was conjectured by the mathematician Eugene Charles Catalan in 1844 and proven in 2002 by Preda Mihailescu. To understand the conjecture, notice that 23 and 32 are two powers of natural numbers, whose values 8 and 9 respectively are consecutive. The conjecture states that this is the only case of two consecutive powers. That is to say, that the only solution in the natural numbers of xa – yb = 1, for x, a, y, b > 1 is x = 3, a = 2, y = 2, b = 3

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