Question: Show that an integer (N) is congruent modulo 9 to the sum of its decimal digits. For example, (475 equiv 4+7+5 equiv 16 equiv 1+6

Show that an integer $N$ is congruent modulo 9 to the sum of its decimal digits. For example, $475 \equiv 4+7+5 \equiv 16 \equiv 1+6 \equiv 7(\bmod 9)$. This is the basis for the familiar procedure of "casting out 9's" when checking computations in arithmetic.

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