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PUMaC 2013 · 数论（B 组） · 第 1 题

PUMaC 2013 — 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 ] If p, q and r are primes with pqr = 7( p + q + r ), find p + q + r . n
解析
  1. [ 3 ] If p, q and r are primes with pqr = 7( p + q + r ), find p + q + r . Solution Without loss of generality, we see that we must have p = 7. Next, qr = 7 + q + r iff ( q − 1)( r − 1) = 8. The only prime solution is ( q, r ) = (3 , 5) up to permutation. Then p + q + r = 15. n