OPM 1998

A chicken breeder went to check what price per chick he had charged the previous year. He found an invoice, half erased, which read: $72$ chickens sold for $*679*$ escudos" (the digits of the units and tens of thousands were illegible). What price did each chick sell for last year?

Could the set $\{1,2,3,...,3000\}$ contain a subset of $2000$ elements such that none of them is twice the size of another?

Let $a_0$ be a positive real number and consider the general term sequence $a_n$ defined by $$a_n =a_{n-1} + \frac{1}{a_{n-1}} \,\, n=1,2,3,...$$ Prove that $a_{1998} > 63$ .