Let's create another set:
a1=a-b, b1=b-c, c1=c-d, d1=d-a;
from the above set we can create in similar fashion a2, b2,c2, and d2,
then a3, b3,c3, and d3, etc ...
Prove that if none of the numbers a100, b100, c100, and d100, is more than 1012 then a=b=c=d=0.