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题 1 给定一个非负整数n及两个实数a和c ,求证 :存在无限多个实系数一元多项式P(x) ,使得对每一个x∈R ,都有P(x) +P( 1 -x) =(a·x2 -a·x +c) n。题 2 确定所有的有序非负整数组 (m ,n ,t) ,使得存在至少一个实系数一元多项式P(x) ,对每一个x∈R ,都有P(x) +xm·P( 1 -x) =
Problem 1 Given a non-negative integer n and two real numbers a and c, verify that there are infinitely many real-valued polynomials P(x) such that for each x∈R, there is P(x) + P( 1 -x) = (a·x2 -a·x +c) n. Problem 2 determines all ordered non-negative integer groups (m,n,t) such that there is at least one real coefficient polynomial P(x) with P(x) +xm·P (for each x∈R). 1 -x) =