Comments on Fermat's Last Theorem / Beal's Conjecture

• Be careful not to assume special properties of integers; for example if n is the exponent you cannot say n = phi(m) where phi is the totient function, as the only odd integer in the image of phi is 1.

• Be very careful with the algebra: often a dropped minus sign leads to a contradiction (inconsistent system of equations), but when the correct sign is used a tautology results.

• Simplify your argument and do a special case or two; run through it for n=3 and n=7.

• Do not use the same symbol to represent two different free variables, thereby losing a degree of freedom

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/