MathDB

Problem 9

Part of 2023 VN Math Olympiad For High School Students

Problems(2)

nice problem about 2 Lemoine points, concurrent

Source: 2023 Viet Nam math olympiad for high school students D1 P9

3/20/2023
Given a quadrilateral ABCDABCD inscribed in (O)(O). Let L,JL, J be the Lemoine point of △ABC\triangle ABC and △ACD\triangle ACD.
Prove that: AC,BD,LJAC, BD, LJ are concurrent.
geometry
(x(x+1))^{2^{2023}}+1is irreducible in Q[x]

Source: 2023 Viet Nam math olympiad for high school students D2 P9

3/25/2023
Prove that: the polynomial(x(x+1))22023+1(x(x+1))^{2^{2023}}+1is irreducible in Q[x].\mathbb{Q}[x].
algebra