The only constitutional requirements for eligibility to be president are birth within the United States, being age 35 or above and having 14 years residence in the United States. PERIOD
And with that statement James has repealed Article II, Section 1, Clause 5.
Clause 5: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
http://www.house.gov/house/Constitution/Constitution.html
not a Cornell website, but a government website