Let n≥2 be a positive integer and {xi}i=0n a sequence such that not all of its elements are zero and there is a positive constant Cn for which:
(i) x1+⋯+xn=0, and
(ii) for each i either xi≤xi+1 or xi≤xi+1+Cnxi+2 (all indexes are assumed modulo n).
Prove that
a) Cn≥2, and
b) Cn=2 if and only 2∣n. algebrainequalitiesSequence