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HMMT 二月 2000 · ORAL 赛 · 第 6 题

HMMT February 2000 — ORAL Round — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [45] Prove that every multiple of 3 can be written as a sum of four cubes (positive or negative).
解析
  1. Any multiple of 3 can be written as 6 k or 6 k + 15. Now, 6 k = ( k + 1) + ( k − 1) + 3 3 3 3 3 3 ( − k ) + ( − k ) . 6 k + 15 = ( k + 2) + ( − k + 2) + (2 k − 1) + ( − 2 k ) . 1