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Part of 2005 Bosnia and Herzegovina Team Selection Test

Problems(1)

Prove that permutation is identical

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

10/6/2017
If for an arbitrary permutation (a1,a2,...,an)(a_1,a_2,...,a_n) of set 1,2,...,n{1,2,...,n} holds ak2ak+1≤k+2\frac{{a_k}^2}{a_{k+1}}\leq k+2, k=1,2,...,n−1k=1,2,...,n-1, prove that ak=ka_k=k for k=1,2,...,nk=1,2,...,n
permutationsidenticalset theory