MathDB

RMO KV P-5

Source:

October 29, 2023

algebraravi s substitutiongeometryperimeter

Problem Statement

The side lengths

a,b,c

of a triangle

ABC

are positive integers. Let:\\

T_{n}=(a+b+c)^{2n}-(a-b+c)^{2n}-(a+b-c)^{2n}+(a-b-c)^{2n}

for any positive integer

n

. If

\frac{T_{2}}{2T_{1}}=2023

and

a>b>c

, determine all possible perimeters of the triangle

ABC