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PUMaC 2011 · 数论（B 组） · 第 1 题

PUMaC 2011 — Number Theory (Division B) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 3 ] What is the largest prime factor of 7999488?
解析
  1. Notice that 7999488 suspiciously close to 8000000. In fact, 7999488 = 8000000 − 512 = 3 9 9 3 3 200 − 2 = 2 (25 − 1). We can either factor this as a difference of cubes, as 25 − 1 = 2 3 2 3 6 (25 − 1)(25 +25+1) = 24 · 651 = 2 · 3 · 7 · 31, or as a difference of squares, since 25 − 1 = 5 − 1. Therefore, 31 is the largest prime factor.