In 1842 the Belgian mathematician Eugene Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy 0 and p, q >=2.
In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must...
In 1842 the Belgian mathematician Eugene Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years...
