MathDB

Problem 1

Part of 2023 VN Math Olympiad For High School Students

Problems(2)

symmedian ratio

Source: 2023 Viet Nam math olympiad for high school students D1 P1

3/25/2023
Given a triangle ABCABC with ADAD is the A−A-symmedian (D(D is on the side BC).BC).
Prove that: DBDC=AB2AC2.\dfrac{DB}{DC}=\dfrac{AB^2}{AC^2}.
geometry
(x-1)(x-2)(x-3)-1 is irreducible in Z[x]

Source: 2023 Viet Nam math olympiad for high school students D2 P1

3/25/2023
Prove that the polynomialP(x)=(x−1)(x−2)(x−3)−1P(x)=(x-1)(x-2)(x-3)-1is irreducible in Z[x].\mathbb{Z}[x].
algebra