By Ching-Li Chai
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In 1842 the Belgian mathematician Eugène Charles Catalan requested no matter if eight and nine are the one consecutive natural powers of non-zero integers. one hundred sixty years after, the query used to be replied affirmatively through the Swiss mathematician of Romanian foundation Preda Mihăilescu. In different phrases, 32 – 23 = 1 is the single answer of the equation xp – yq = 1 in integers x, y, p, q with xy ≠ zero and p, q ≥ 2.
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Compactification of Siegel Moduli Schemes (London Mathematical Society Lecture Note Series) by Ching-Li Chai