Determine all possible value(s) of a 15-digit base ten positive integer N which is constituted entirely by the digits 2 and 3, such that N is divisible by the base ten repunit R₇.

DECLARE SUB build ()
DEFDBL A-Z
DIM SHARED dig(15), placeVal, psn, tot

placeVal = 100000000000000#: psn = 1

build

SUB build
 FOR d = 2 TO 3
  dig(psn) = d
  tot = tot + d * placeVal
  IF psn = 15 THEN
    q = INT(tot / 1111111)
    totMod = tot - q * 1111111
    IF totMod = 0 THEN
      FOR i = 1 TO 15
        PRINT dig(i);
      NEXT
      PRINT , q
    END IF
  ELSE
   psn = psn + 1: placeVal = placeVal / 10
   build
   psn = psn - 1: placeVal = placeVal * 10
  END IF
  tot = tot - d * placeVal
 NEXT
END SUB

finds

2  3  3  3  3  3  3  2  3  3  3  3  3  3  2             210000012

being the digits of the answer and the quotient upon dividing by 1111111.

Posted by Charlie on 2010-01-07 15:57:38