MathDB

2

Part of 2019 China National Olympiad

Problems(1)

Chain of pythagorean triplets

Source: China Mathematical Olympiad 2019 Q2

11/14/2018
Call a set of 3 positive integers {a,b,c}\{a,b,c\} a Pythagorean set if a,b,ca,b,c are the lengths of the 3 sides of a right-angled triangle. Prove that for any 2 Pythagorean sets P,QP,Q, there exists a positive integer m≥2m\ge 2 and Pythagorean sets P1,P2,…,PmP_1,P_2,\ldots ,P_m such that P=P1,Q=PmP=P_1, Q=P_m, and ∀1≤i≤m−1\forall 1\le i\le m-1, Pi∩Pi+1≠∅P_i\cap P_{i+1}\neq \emptyset.
number theoryHi