Comments on the 3x+1 Problem

• Make sure you handle all cases -- it is very easy to accidentally assume an iteration has a certain behavior.

• Be careful not to assume any special properties of a generic number.

• It is not known that every integer eventually iterates to a number less than or equal to itself.

Comments on specific problems.

• Fermat's Last Theorem / Beal's Conjecture

• The Riemann Hypothesis

• The 3x+1 Problem

• Odd Perfect Numbers

• Twin Primes / Goldbach Conjecture

Main page: https://web.williams.edu/Mathematics/sjmiller/public_html/jntnewpolicy/