MathDB
n -gonal Pythagorean triples, P(n, r) = (n - 2)r^2/2 - (n - 4) r/2

Source: Indian Postal Coaching 2009 set 1 p4

May 26, 2020
algebraanglesminmaxnumber theory

Problem Statement

For positive integers n≥3n \ge 3 and r≥1r \ge 1, define P(n,r)=(n−2)r22−(n−4)r2P(n, r) = (n - 2)\frac{r^2}{2} - (n - 4) \frac{r}{2} We call a triple (a,b,c)(a, b, c) of natural numbers, with a≤b≤ca \le b \le c, an nn-gonal Pythagorean triple if P(n,a)+P(n,b)=P(n,c)P(n, a)+P(n, b) = P(n, c). (For n=4n = 4, we get the usual Pythagorean triple.)
(a) Find an nn-gonal Pythagorean triple for each n≥3n \ge 3.
(b) Consider all triangles ABCABC whose sides are nn-gonal Pythagorean triples for some n≥3n \ge 3. Find the maximum and the minimum possible values of angle CC.
Back to ProblemsView on AoPS