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HMMT 十一月 2013 · 冲刺赛 · 第 12 题

HMMT November 2013 — Guts Round — Problem 12

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 8 ] Given that 62 + 122 = 18728, find positive integers ( n, m ) such that n + m = 9364. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT NOVEMBER 2013, 9 NOVEMBER 2013 — GUTS ROUND
解析
  1. [ 8 ] Given that 62 + 122 = 18728, find positive integers ( n, m ) such that n + m = 9364. 2 2 2 2 a + b a − b 2 a +2 b a + b 2 2 2 2 Answer: (30 , 92) OR (92 , 30) If a + b = 2 c , then ( ) + ( ) = = = c . Thus, 2 2 4 2 62+122 122 − 62 n = = 92 and m = = 30 works. 2 2