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Is it true ??

Source: Bulgaria TST 2003 P4

September 8, 2012

number theory proposednumber theory

Problem Statement

Is it true that for any permulation

a_1,a_2.....,a_{2002}

of

1,2....,2002

there are positive integers

m,n

of the same parity such that

0<m<n<2003

and

a_m+a_n=2a_{\frac {m+n}{2}}

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