MathDB

4

Part of 2004 APMO

Problems(1)

Floor function

Source: APMO 2004

4/8/2006
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.
functionfloor functionmodular arithmeticnumber theoryrelatively primenumber theory unsolved