Let's create another set:

a

_{1}=a-b, b

_{1}=b-c, c

_{1}=c-d, d

_{1}=d-a;

from the above set we can create in similar fashion a

_{2}, b

_{2},c

_{2}, and d

_{2},

then a

_{3}, b

_{3},c

_{3}, and d

_{3}, etc ...

Prove that if none of the numbers a_{100}, b_{100}, c_{100}, and d_{100}, is more than 10^{12} then** a=b=c=d=0**.