## Catalan's conjecture

If you write out all the $n$th powers of natural numbers for $n \gt 1$ ("higher powers") in increasing order you get a sequence like this: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, 216, 225, … If you keep computing more numbers in […]