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D-Number

A Natural Number $n>3$ such that

\begin{displaymath}
n\vert(a^{n-2}-a)
\end{displaymath}

whenever $(a,n)=1$ ($a$ and $n$ are Relatively Prime) and $a\leq n$. There are an infinite number of such numbers, the first few being 9, 15, 21, 33, 39, 51, ... (Sloane's A033553).

See also Knödel Numbers


References

Makowski, A. ``Generalization of Morrow's $D$-Numbers.'' Simon Stevin 36, 71, 1962/1963.

Sloane, N. J. A. Sequence A033553 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.




© 1996-9 Eric W. Weisstein
1999-05-24