[math-fun] N/b gives 'a' as remainder

Hello MathFun, If I split integer N into two substrings a and b, (for instance N=423156 --> a=423 and b=156) ... I have almost always b as a remainder of N/a. (This works also if I split N=423156 into a=42315 and b=6 ... or if I split N=423156 into a=4231 and b=56, etc.) The only exceptions for N are (I think): 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99. (which are integers < 100 with equal digits or digits in increasing order) Now, are there integers N with N/b giving 'a' as remainder? (as usual, no integers a or b with leading zero -- like 09) Best, É.