25 May
2016
25 May
'16
3:15 a.m.
* Victor Miller <victorsmiller@gmail.com> [May 25. 2016 10:33]:
The language of numbers in base b which leave a set of remainders modulo d is a regular language, so you can recognize it via a finite automaton.
Victor [...]
For every base b and every (tentative) divisor d one can obtain a periodic sequence of weights such that the weighted sum of digits tells whether a base-b number is divisible by d. IIRC the sequence of weights corresponds to the sequence b^n mod d. I once wrote that up (on paper) but that is certainly lost. My warmup exercise was to find for base b the rules for d = b - 1 and d = b + 1. Cannot recall the details from the top of my head, should be easy, though. Best regards, jj