What is the definition of isotopes?

I- Isotopes are atoms of the same element that have the same atomic number but different mass numbers.
II- Isotopes are atoms of different elements that have the same atomic number but different mass numbers.
III- Isotopes are atoms of the same element that have the same mass number but different atomic numbers.
a) Only I is correct.
b) Only II is correct.
c) Only III is correct.
d) I and III are correct.
e) II and III are correct.