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Prove that permutation is identical

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 2 day 2

October 6, 2017

permutationsidenticalset theory

Problem Statement

If for an arbitrary permutation

(a_1,a_2,...,a_n)

of set

{1,2,...,n}

holds

\frac{{a_k}^2}{a_{k+1}}\leq k+2

k=1,2,...,n-1

, prove that

a_k=k

for

k=1,2,...,n