Miklos Schweitzer 1950_4
Source: first round of 1950
October 2, 2008
algebrapolynomialalgebra proposed
Problem Statement
Find the polynomials 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