MathDB

Problem 4

Part of 2023 VN Math Olympiad For High School Students

Problems(2)

the length of symmedian and angle bisector

Source: 2023 Viet Nam math olympiad for high school students D1 P4

3/25/2023
Determine whether or not the length of symmedian is not greater than the length of the angle bisector drawn from the same vertex?
geometry
irreducible in Z[x] iff irreducible in Q[x]

Source: 2023 Viet Nam math olympiad for high school students D2 P4

3/25/2023
Prove that: a polynomial is irreducible in Z[x]\mathbb{Z}[x] if and only if it is irreducible in Q[x].\mathbb{Q}[x].
algebrapolynomial