5

Part of 2000 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2000 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 2000

T_m

be a number of non-congruent triangles which perimeter is

m

and all its sides are positive integers. Prove that:

a)

T_{1999} > T_{2000}

b)

T_{4n+1}=T_{4n-2}+n

(n \in \mathbb{N})

geometryperimetercongruent