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No two distinct elements have the same atomic number. The atomic number is the number of protons an element has and is what makes it that particular unique element.

Isotopes do have the same atomic number however they belong to the same element because an isotope is just a form of the element with more or less neutrons in the nucleus, not a different element.

An example would be Hydrogen, it has three Isotopes:

Hydrogen-1 its nucleus is composes of just a single proton.

Hydrogen-2 or deuterium has a proton and a neutron in its nucleus.

Hydrogen-3 or tritium has a proton and two neutrons in its nucleus.

Notice that they all have just one proton, this by definition makes them all hydrogen atoms, and considered to be the same element.

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