Take the 2-minute tour ×  If $(m, 10) = 1$, choose $b$ so that
$10 b \equiv 1 \pmod m$. Then $n \equiv 0 \pmod m$ if and only
if $n' + ba_0 \equiv 0 \pmod m$, where $a_0$ is the unit's digit
of $n$, and $n'=(n-a_0)/10$. First generalize this and tell me
how to extend this theorem to general divisibility tests of
other numbers by a single formula or method or procedure.
share|improve this question What are n' and $a_0$? –  user7530
Oct 4 '11 at 7:23 I suspect that $a_0$ is the last (one’s) digit
of $n$ and that $n'=(n-a_0)/10$, the number that you get when
you erase the last digit of $n$; is that correct? –  Brian M.
Scott Oct 4 '11 at 7:49 @Brain M. Scott! Your suspected one is
very right. The last digit is $a_0$. –  gandhi Oct 4 '11 at 8:09
Edited to include Brian's interpretations. –  Gerry Myerson Oct
4 '11 at 12:11 add comment  2 Answers  I suppose a
generalization would be, if $\gcd(m,r)=1$, choose $b$ so that
$rb\equiv1\pmod m$. Then $n\equiv0\pmod m$ if and only if
$n'+ba_0\equiv0\pmod m$, where $a_0$