Given a set of 4 random integers a,b,c,d.
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.

Following Ch's remark:

"Given a set of 4 random integers a,b,c,d."

should be replaced by

"Given a set of 4 distinct  integers a,b,c,d."

Thank you,  Charlie.

Posted by Ady TZIDON on 2015-03-23 23:33:44