IMO 1984 LL BEL5

For a real number x, let [x] denote the greatest integer not

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IMO 1984 LL BEL5

Origin: BEL

Problem

For a real number x, let [x] denote the greatest integer not exceeding x. If m \geq3, prove that m(m + 1) 2(2m −1)

m + 1 .