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Determine f(2000)

Source:

January 22, 2011
functioninductionalgebra unsolvedalgebra

Problem Statement

Define a function f:N→N0f:\mathbb{N}\rightarrow\mathbb{N}_0 by f(1)=0f(1)=0 and f(n)=\max_j\{ f(j)+f(n-j)+j\} \forall\, n\ge 2 Determine f(2000)f(2000).
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