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Casting Out Nines

An elementary check of a Multiplication which makes use of the Congruence $10^n\equiv 1 $ (mod 9) for $n\geq
2$. From this Congruence, a Multiplication $ab=c$ must give

\begin{displaymath}
a\equiv \sum a_i = a^*
\end{displaymath}


\begin{displaymath}
b\equiv \sum b_i = b^*
\end{displaymath}


\begin{displaymath}
c\equiv \sum c_i = c^*,
\end{displaymath}

so $ab \equiv a^*b^*$ must be $\equiv c^*$ (mod 9). Casting out nines is sometimes also called ``the Hindu Check.''


References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 28-29, 1996.




© 1996-9 Eric W. Weisstein
1999-05-26