Challenge - Keypad puzzle

[pinkman]

Following Albert’s idea using congruence:

Because:
1000≡-1 (mod 11)
100≡1 (mod 11)
10≡-1 (mod 11)
1≡1 (mod 11)

Then:
A*1000+B*100+C*10+D≡-A+B-C+D (mod 11)
-A+B-C+D=-(A-B+C-D)=0 because the sum of the subtraction of vertices is always 0.
So : A*1000+B*100+C*10+D≡0 (mod 11)

Original idea and demonstration: https://twitter.com/fermatslibrary/statu...55681?s=21