MathDB
Miklos Schweitzer 1950_4

Source: first round of 1950

October 2, 2008
algebrapolynomialalgebra proposed

Problem Statement

Find the polynomials f(x) f(x) having the following properties: (i) f(0) \equal{} 1, f'(0) \equal{} f''(0) \equal{} \cdots \equal{} f^{(n)}(0) \equal{} 0 (ii) f(1) \equal{} f'(1) \equal{} f''(1) \equal{} \cdots \equal{} f^{(m)}(1) \equal{} 0