Texas College Mathematics Journal

Vol. 2 (2005), pp. 1-9.

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**Subtractive Black Holes and Black Loops**

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MURRAY H. SIEGEL, WASIN SO AND PETER A. COOPER

**MSC (2000):** Primary 97 - 02

**Key words:** Subtractive process, Kaprekar constant, unique
terminations

**Abstract: **Subtractive black holes and black loops are generalizations
of Kaprekar's constants. When the subtractive Kaprekar routine is applied to an
n-digit number a termination in the form of a black hole or black loop is
reached. If all n-digit numbers for a specific value of n, other than numbers
where all digits are the same, result in the same black hole then that number is
a Kaprekar constant. The process and its results provide a rich environment for
conjecture and proof.

Mathematics & Computer Science Division, South Carolina Governor's School
for Science & Mathematics, SC

E-mail address: siegel@gssm.k12.sc.us

Received by Editor: April 18, 2004 and, in revised form August 3,
2005.

Posted: August 17, 2005.

© Copyright 2005