MathDB

2

Part of 1999 Tuymaada Olympiad

Problems(2)

Tuymaada 1999, Q2

Source: Tuymaada 1999, Q2

7/31/2012
Find all polynomials P(x)P(x) such that P(x3+1)=P(x3)+P(x2). P(x^3+1)=P(x^3)+P(x^2).
Proposed by A. Golovanov
algebrapolynomialalgebra unsolved
Tuymaada 1999, Q6

Source: Tuymaada 1999, Q6

7/31/2012
Can the graphs of a polynomial of degree 20 and the function y=1x40\displaystyle y={1\over x^{40}} have exactly 30 points of intersection?
Proposed by K. Kokhas
algebrapolynomialfunctioncalculusderivative