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HMMT 十一月 2012 · GEN 赛 · 第 1 题

HMMT November 2012 — GEN Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

[3] What is the sum of all of the distinct prime factors of 253−272?

解析

英文解析

  1. [ 3 ] What is the sum of all of the distinct prime factors of 25 − 27 ?
    3 2 6 6 3 3 3 3 2 2
    Answer: 28 We note that 25 − 27 = 5 − 3 = (5 − 3 )(5 + 3 ) = (5 − 3)(5 + 5 · 3 + 3 )(5 +
    2 2 2 3
    3)(5 − 5 · 3 + 3 ) = 2 · 7 · 2 · 19, so the sum of the distinct prime factors is 2 + 7 + 19 = 28. 2