MathDB

7

Part of 2024 Tuymaada Olympiad

Problems(2)

Easier version of Tuymaada seniors P7

Source: Tuymaada 2024 Juniors P7

7/10/2024
Given are quadratic trinomials ff and gg with integral coefficients. For each positive integer nn there is an integer kk such that f(k)g(k)=n+1n.\frac{f(k)}{g(k)}=\frac{n + 1}{n}. Prove that ff and gg have a common root. Proposed by A. Golovanov
algebraPolynomials
Irreducibilty Polynomials

Source: Tuymadaa Senior 2024 P7

7/7/2024
Given are two polynomial ff and gg of degree 100100 with real coefficients. For each positive integer nn there is an integer kk such that f(k)g(k)=n+1n.\frac{f(k)}{g(k)}=\frac{n+1}{n}. Prove that ff and gg have a common non-constant factor.
algebrapolynomial