# Number is congruent to alternating sum of digits mod 11

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• December 2nd 2009, 07:33 PM
ChrisBickle
Number is congruent to alternating sum of digits mod 11
OK here is the problem posed to me and this instructor does like to throw things in that are not always true so that may be the case but i tried a few cases and it seems to work. The question is: For any natural number n, n is congruent to the alternating sum of its digits mod 11. I have no idea where to even start with this. Any help would be greatly appreciated.
• December 2nd 2009, 07:36 PM
chiph588@
Given that $a=a_n a_{n-1} ... a_1 a_0$, then $a=\sum_{i=0}^n a_i \cdot 10^i \equiv \sum_{i=0}^n a_i \cdot (-1)^i \mod{11}$, since $10 \equiv -1 \mod{11}$.