 # ⓘ Intermediate value theorem. The intermediate value theorem says that if a function, f {\displaystyle f}, is continuous over a closed interval }, and is equal to .. ## ⓘ Intermediate value theorem

The intermediate value theorem says that if a function, f {\displaystyle f}, is continuous over a closed interval }, and is equal to f {\displaystyle f} and f {\displaystyle f} at either end of the interval, for any number, c, between f {\displaystyle f} and f {\displaystyle f}, we can find an x {\displaystyle x} so that f = c {\displaystyle f=c}.

This means that if a continuous functions sign changes in an interval, we can find a root of the function in that interval. For example, if f 1 = − 1 {\displaystyle f1=-1} and f 2 = 2 {\displaystyle f2=2}, we can find an x {\displaystyle x} in the interval } that is a root of this function, meaning that for this value of x, f x = 0 {\displaystyle fx=0}, if f {\displaystyle f} is continuous. This corollary is called Bolzanos theorem.

• other intermediate values from key generation. Although this form allows faster decryption and signing by using the Chinese Remainder Theorem CRT it