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Let T(n) denotes the number of non-congr...

Let T(n) denotes the number of non-congruent triangles with integer side lengths and perimeter n. Thus `T(1)=T(2)=T(3)=T(4)=0`, while `T(5)=1`. Prove that: (i) `T(2006)ltT(2009)` ii) `T(2005)=T(2008)`

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