It was once presented to me as a fact, and they asked for a proof, that n|k(n) if and only if n is prime. I immediately said that it couldn't possibly be true, so I was challenged to find a counter-example.
This was in the days before languages like Python, with arbitrary precision integers. I used C to find the first place it failed, and indeed, all counter-examples less than 2^32.
There aren't many, and they have interesting things in common. It's a fascinating mathematical and programmatic playground.
This was in the days before languages like Python, with arbitrary precision integers. I used C to find the first place it failed, and indeed, all counter-examples less than 2^32.
There aren't many, and they have interesting things in common. It's a fascinating mathematical and programmatic playground.