If two integers are either both negative or both positive, we can say they have the same sign.
How about two integers that are either both odd or both even? Is there any term for them?
Expanding on a comment by @TomKern: The word you're looking for is parity.
You can see it in most standard English dictionaries, such as Merriam-Webster, here:
4 a: the property of an integer with respect to being odd or even
3 and 7 have the same parity
b(1): the state of being odd or even used as the basis of a method of detecting errors in binary-coded data (see binary entry 2 sense 5)
b(2): parity bit
And here's the Wikipedia article on the subject.
In mathematics, parity is the property of an integer of whether it is even or odd.
And here's the equivalent question at Stack Exchange: English Language & Usage.