Vckbaseblog is a mathematical problem-(how to determine the multiples of 11)

Author: zfive5 (zhaozidong)
Email: zfive5@yahoo.com.cn

Noon break, trainer

N = A0 + A1 * 10 + A2 * 100 + A3 * 1000 +... + am * 10 ^ m +...

N = A0 + A1 * (10 + 1) + A2 * (100-1) + A3 (1000 + 1) +... am * (10 ^ m-(-1) ^ m)

-(A1-a2 + A3 + ....)

10 ^ M-1 = (11-1) ^ m-1 (10 ^ m-1 is a multiple of 11 when M is an even number, according to the quadratic expansion formula)
10 ^ m + 1 = (11-1) ^ m + 1 (when M is an odd number, 10 ^ m + 1 is a multiple of 11, according to the quadratic expansion formula)

N = a0-a1 + a2-a3... + 11 * x

If n is a multiple of 11, the sum of all odd digits minus the sum of even digits is a multiple of 11!