If upperBound and lowerBound are called on the same array to search for the same value, like this:

int idx$1=$ BinarySearch.lowerBound$($a$,$ value$)$;

int idx$2=$ BinarySearch.upperBound$($a$,$ value$)$;

and the returned indices are the same $($that is$,$ idx$1==$ idx$2),$ then which of these is true?

There are no elements of a that are equal to value.

This can't happen; it is impossible for idx$1$ and idx$2$ to be equal.

There is exactly one element of a that is equal to value.