Proof - Why every integer is congruent to sum of its digits modulo 9

Let the number have 'k' digits.
So the number is:
d_k.10^k + d_(k-1).10^(k-1) ... d_0.10^0
Take mod 9.
Any power of 10 mod 9 = 1
so the result is:
d_k + d_(k-1) ... d_0
which is sum of its digits.

So any 2 integers which have same digits will have same remainder upon division by 9.

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