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HMMT 十一月 2025 · 冲刺赛 · 第 8 题

HMMT November 2025 — Guts Round — Problem 8

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [7] Compute the sum of the distinct prime factors of 20202525.
解析
  1. We know n is a fourth power, so its prime factorization can be written as p p . . . where each e i 1 2 Q 4 2 is 1 mod 4. Since ( e + 1) = 2025 = 3 5 , we must write 2025 as a product of 1 mod 4 factors. i i 4 4 2 2 2 The best way to do so is 9 · 9 · 5 · 5, yielding n = 2 · 3 · 5 · 7 = 1260 = 1587600 . (This is a 12 4 4 2 lot better than 25 · 9 · 9, which yields 2 · 3 · 5 = 14400 .)