MathDB
I 19

Source:

May 25, 2007
floor functionfunctiontrigonometry

Problem Statement

Let a,b,ca, b, c, and dd be real numbers. Suppose that ⌊na⌋+⌊nb⌋=⌊nc⌋+⌊nd⌋\lfloor na\rfloor +\lfloor nb\rfloor =\lfloor nc\rfloor +\lfloor nd\rfloor for all positive integers nn. Show that at least one of a+ba+b, a−ca-c, a−da-d is an integer.
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