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HMMT 二月 2024 · ALGNT 赛 · 第 8 题

HMMT February 2024 — ALGNT Round — Problem 8

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Let ζ = cos + i sin . Suppose a > b > c > d are positive integers satisfying 13 13 √ a b c d | ζ + ζ + ζ + ζ | = 3 . Compute the smallest possible value of 1000 a + 100 b + 10 c + d .
解析
  1. Let ζ = cos + i sin . Suppose a > b > c > d are positive integers satisfying 13 13 √ a b c d | ζ + ζ + ζ + ζ | = 3 . Compute the smallest possible value of 1000 a + 100 b + 10 c + d . Proposed by: Rishabh Das Answer: 7521 ′ ′ ′ a b c Solution: We may as well take d = 1 and shift the other variables down by d to get | ζ + ζ + ζ +1 | = √