How many integers have the same quotient and remainder after being divided by 13?
Let the remainder be X after being divided by 13, then the number with the same quotient and remainder after being divided by 13 is: 13X + x = (13 + 1) x = 14x, because x < 13, so 100 < 14x < 182, the solution is 507 < x < 13, that is, x can be 8, 9, 10, 11, 12; so there are five numbers with the same quotient and remainder after being divided by 13, namely 13 × 8 + 8 = 112, 13 × 9 + 9 = 126, 13 × 10 + 10 = 140, 13 × 11 + 11 = 154, 13 × 12 + 12 = 168 There are five numbers with the same division quotient and remainder