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area of triangle with integer sidelenghts, t_{n + 2} = 14t_{n + 1} - t_n,

Source: Mathley 2014.1 p2

August 19, 2020
geometryTriangleIntegersSequencealgebraarea of a triangle

Problem Statement

Given the sequence (tn)(t_n) defined as t0=0t_0 = 0, t1=6t_1 = 6, tn+2=14tn+1−tnt_{n + 2} = 14t_{n + 1} - t_n. Prove that for every number n≥1n \ge 1, tnt_n is the area of a triangle whose lengths are all numbers integers.
Dang Hung Thang, University of Natural Sciences, Hanoi National University.
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