Catalan's Conjecture - Numberphile
With Dr Holly Krieger from Murray Edwards College, University of Cambridge. Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile More links & stuff in full descriptio...
==========
So, today I'm going to tell you about what's called Catalan's conjecture. So even though it's called a conjecture, it's actually known, so this was proved by a mathematician about 15 years ago. And it's a question about, or a statement about, perfect powers, okay? So... What do I mean by perfect powers, first of all? I mean, take some whole number - 1, 2, 3, so on - and raise it to a power which is larger than 1, okay, so squares, cubes and so on. So if you start to write these things down, 1 is a perfect power, in fact a power of itself to any exponent, 2 is not, 3 is not, But then we get 4, which is 2 squared. Then we have to go up to I guess 8, which is 2 cubed, and 9 is 3 squared, and 16, 25 Am I gonna run into any cub...
==========
So, today I'm going to tell you about what's called Catalan's conjecture. So even though it's called a conjecture, it's actually known, so this was proved by a mathematician about 15 years ago. And it's a question about, or a statement about, perfect powers, okay? So... What do I mean by perfect powers, first of all? I mean, take some whole number - 1, 2, 3, so on - and raise it to a power which is larger than 1, okay, so squares, cubes and so on. So if you start to write these things down, 1 is a perfect power, in fact a power of itself to any exponent, 2 is not, 3 is not, But then we get 4, which is 2 squared. Then we have to go up to I guess 8, which is 2 cubed, and 9 is 3 squared, and 16, 25 Am I gonna run into any cub...
