MathDB

a) Given a quartet of positive numbers

(a,b,c,d)

. It is transformed to the new one according to the rule:

a'=ab, b' =bc, c'=cd,d'=da

. The second one is transformed to the third according to the same rule and so on. Prove that if at least one initial number does not equal 1, than You can never obtain the initial set.
b) Given a set of

2^k

(

k

-th power of two) numbers, equal either to

1

or to

-1

. It is transformed as that was in the a) problem (each one is multiplied by the next, and the last -- by the first. Prove that You will always finally obtain the set of positive units.

Problem Statement