MathDB
Floor function

Source: APMO 2004

April 8, 2006
functionfloor functionmodular arithmeticnumber theoryrelatively primenumber theory unsolved

Problem Statement

For a real number xx, let ⌊x⌋\lfloor x\rfloor stand for the largest integer that is less than or equal to xx. Prove that ⌊(n−1)!n(n+1)⌋ \left\lfloor{(n-1)!\over n(n+1)}\right\rfloor is even for every positive integer nn.
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