Each of p and q is a 6-digit base ten positive integer with no leading zero. The 12-digit number that is obtained by writing p and q side-by-side is divisible by the product p*q.
Determine all possible pair(s) (p, q) for which this is possible.
(In reply to
Full solution by Steve Herman)
Congratulations to all! This solution showed up on my final list (for p and q of six digits), but so did about 25 others which were within the precison limits I could check by program (limited to 17 significant digits). The Microsoft calculator ( which I think has about 31 significant digits) showed the final division of the 12-digit by the product of p*q only "coming close" for the others I checked manually. As I speculated, q seemed as though it had to be a multiple of p -- one of the very near misses was 166667 and 500001.
re: Full solution
