IMO 1985 LL FRG29

Call a four-digit number (xyzt)B in the number system with

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IMO 1985 LL FRG29

Origin: FRG

Problem

Call a four-digit number (xyzt)B in the number system with base B stable if (xyzt)B = (dcba)B −(abcd)B, where a \leqb \leqc \leqd are the digits of (xyzt)B in ascending order. Determine all stable numbers in the number system with base B. (FRG 2a) The same problem with B = 1985. (FRG 2b) With assumptions as in FRG 2, determine the number of bases B \leq1985 such that there is a stable number with base B.