Editing Divisibility rule (section)

===Divisibility by 11 ===

'''Method'''

In order to check divisibility by 11, consider the alternating sum of the digits. For example with 907,071:

<math>9-0+7-0+7-1 = 22 = 2\times 11, </math>

so 907,071 is divisible by 11.

We can either start with <math>-</math> or <math>+</math> since multiplying the whole by <math>-1</math> does not change anything.

'''Proof of correctness of the method'''

Considering that <math>10 \equiv -1 \bmod 11</math>, we can write for any integer:

<math> \overline{a_{n} a_{n-1}...a_1 a_0} = \sum_{i=0}^n a_i 10^i \equiv \sum_{i=0}^n (-1)^i a_i \bmod 11.</math>