ILL 1985 Problem 29

a) Call a four-digit number $(xyzt)_B$ in the number system with base $B$ stable if $(xyzt)_B = (dcba)_B - (abcd)_B$ , where $a \leq b \leq c \leq d$ are the digits of $(xyzt)_B$ in ascending order. Determine all stable numbers in the number system with base $B.$ b) With assumptions as in a, determine the number of bases $B \leq 1985$ such that there exists a stable number with base $B.$