Divisibility Rules! Base 2015

Number Theory Level 4

In base 10, the divisiblity rule for 11 works as follows:

Suppose we have a number \(a_6a_5a_4a_3a_2a_1\). Then we know whether this number is divisible by 11 if and only if the numbers in odd places (\(a_1, a_3, a_5\)) and the numbers in even places(\(a_2, a_4, a_6\)) have a difference divisible by 11, i.e. \((a_1+ a_3+ a_5)-(a_2+ a_4+ a_6)\) is divisible by 11.

In base 2015, for how many numbers can this divisibility rule be applied (excluding 1)?

Submit your answer as the sum of all numbers for which this divisibility rule can be applied.


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