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PUMaC 2019 · 数论（B 组） · 第 6 题

PUMaC 2019 — Number Theory (Division B) — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Let f be a polynomial with integer coefficients of degree 2019 such that the following conditions are satisfied: (a) For all integers n , f ( n ) + f ( − n ) = 2. 2 (b) 101 | f (0) + f (1) + f (2) + · · · + f (100). 2 Compute the remainder when f (101) is divided by 101 . ∑ n
解析
  1. Let f be a polynomial with integer coefficients of degree 2019 such that the following conditions are satisfied: