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G(n) = n-G(G(n)), G(0) = 0 , G(k) \ge G(k -1) , G(k -1) = G(k) = G(k +1)

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1996 p1

February 20, 2020

Sequencealgebrainequalities

Problem Statement

A sequence

(G_n)_{n=0}^{\infty}

satisfies

G(0) = 0

and

G(n) = n-G(G(n-1))

for each

n \in N

. Show that (a)

G(k) \ge G(k -1)

for every

k \in N

; (b) there is no integer

k

for which

G(k -1) = G(k) = G(k +1)