Given a strictly increasing infinite sequence {an} of positive real numbers such that for any n∈N: an+2=(an+1−an)√n+n−√nProve that for any C>0 there exist a positive integer m(C) (depended on C) such that am(C)>C.
Source: Kazakhstan NMO 2016, P6
Tags: number theory, algebra
Given a strictly increasing infinite sequence {an} of positive real numbers such that for any n∈N: an+2=(an+1−an)√n+n−√nProve that for any C>0 there exist a positive integer m(C) (depended on C) such that am(C)>C.