This program calculates the Polydivisible numbers. It is inspired by a blog post on republicofmath.com which highlighted a result of Ben Vitale for a 25 digit polydivisible number.
- https://en.wikipedia.org/wiki/Polydivisible_number
- http://www.blog.republicofmath.com/the-number-3608528850368400786036725/
3608528850368400786036725 is the only 25 digit number which satisfies the polydivisibilty (or Vitale) property. It is divisible by 25, it's first 24 digits are divisible by 24, it's first 23 digits are divisible by 23 etc. all the way down to 2. There are NO 26 digit numbers which extend this property.
None to speak of, just run the python scripts through a python2 or 3 interpreter
vitale.py: A python implementation which recursivly calculates these numbers until a zero is found. It plots the number of vitale numbers for each n if matplotlib is available. We use the arbitrary precision of python integers.
vitale-numpy.py: Placeholder for a numpy version of vitale.py. Since we know a-posteriori that 25 is the maximum number of digits we'll encounter int28 or uint128 will comfortably handle all cases, unfortunately these only seem to be in the development versions of numpy at the moment.