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### Catalan's conjecture

The **Catalan conjecture** states that apart from the powers 2^{3} = 8 and 3^{2} = 9 there are no other *real* powers that differ by exactly 1.

##### Explanation

The conjecture was formulated in 1844 by the Belgian mathematician Eugène Charles Catalan. The calculation can be written as

3

^{2}− 2^{3}= 9 − 8 = 1

## HistoryIn 2002 the Romanian mathematician Preda Mihăilescu proved that the only solution of two consecutive powers in the natural numbers for
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