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HMMT 2018 A4

  • Algebra and Number Theory
  • Answer

Distinct prime numbers p,q,rp, q, r satisfy the equation

2pqr+50pq=7pqr+55pr=8pqr+12qr=A2 p q r+50 p q=7 p q r+55 p r=8 p q r+12 q r=A

for some positive integer AA. What is AA ?

Dataset text NuminaMath olympiads. Quoted with source.

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1980

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