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HMMT 十一月 2015 · 冲刺赛 · 第 34 题

HMMT November 2015 — Guts Round — Problem 34

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 20 ] Let n be the second smallest integer that can be written as the sum of two positive cubes in two ( ( ) ) a n different ways. Compute n . If your guess is a , you will receive max 25 − 5 · max , , 0 points, n a rounded up.
解析
  1. [ 20 ] Let n be the second smallest integer that can be written as the sum of two positive cubes in two ( ( ) ) a n different ways. Compute n . If your guess is a , you will receive max 25 − 5 · max , , 0 points, n a rounded up. Proposed by: Alexander Katz Answer: 4104 3 3 3 3 A computer search yields that the second smallest number is 4104 . Indeed, 4104 = 9 + 15 = 2 + 16