If is a continuous function and and

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

f(x)

is a continuous function

\forall x \in R

and

f(x) \in (1, \sqrt{30})

and

g(x) = \left[ \frac{f(x)}{a} \right]

, where

[\cdot]

denotes the greatest integer function, is continuous

\forall x \in R

, then the least positive integral value of

a

is __________.