Only one pair of consecutive whole numbers are both exact powers greater than one
8 is 2 cubed and 9 is 3 squared, making them consecutive whole numbers that are both perfect powers above the first power. In 1844, Belgian mathematician Eugene Catalan conjectured that 8 and 9 are the only such pair that will ever exist — that no other pair of perfect powers can ever sit exactly one apart on the number line. Was Catalan right, and if so, how long did it take anyone to prove it?
Reveal the answer
Catalan was right, but it took 158 years to prove. Romanian mathematician Preda Mihailescu finally proved the conjecture in 2002, using advanced number theory involving cyclotomic fields, showing 3 squared minus 2 cubed equals 1 really is the only solution of that kind with whole-number powers greater than one. The result is now officially known as Mihailescu's theorem.