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Stable four digit numbers

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September 13, 2010
number theory proposednumber theory

Problem Statement

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