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PUMaC 2016 · 代数（B 组） · 第 1 题

PUMaC 2016 — Algebra (Division B) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. for all complex numbers x . Suppose P is the polynomial in S of maximal degree such 0 P that P (1) | 2016. Find P (10). 0 0 1
解析
  1. We have ( x − 1) = 9801, so x − 1 = ± 99. But x cannot be negative, so x = 99 + 1 = 100. Since x is positive, we have x = 10 . Problem written by Eric Neyman. 3 3 3 3 3 3 3 3 3 3