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largest integer [(n+1)a]-[na], a=\sqrt{2013}/\sqrt{2014} (HOMC 2013 J Q3)

Source:

July 25, 2019
floor functionalgebra

Problem Statement

The largest integer not exceeding [(n+1)a]−[na][(n+1)a]-[na] where nn is a natural number, a=20132014a=\frac{\sqrt{2013}}{\sqrt{2014}} is:
(A): 11, (B): 22, (C): 33, (D): 44, (E) None of the above.
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