The smallest natural number for which is an odd function for all is

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The smallest natural number

k

for which

f(x)=\ln\left(x^3+\sqrt{x^6+1}\right)+\sin5x+\left\lfloor\frac{x^2}{k}\right\rfloor

is an odd function for all

x\in[-2\pi,2\pi]

is, where

\lfloor y\rfloor

denotes the greatest integer less than or equal to

y

, (a)

38

(b)

39

(c)

40

(d)

41