Given a set of 4 random integers a,b,c,d.
Let's create another set:
a
_{1}=ab, b
_{1}=bc, c
_{1}=cd, d
_{1}=da;
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.
(In reply to
correction ............... see before solving by Ady TZIDON)
Given that change to the problem, then the item to be proved should be changed to say that one or more of the numbers a100..., d100, will be more than 10^12, as the conditions are already set that the numbers are distinct, and therefore not equal.

Posted by Charlie
on 20150324 07:43:06 