While rummaging through old graduate textbooks on Algebraic Number Theory I stumbled upon one of the claims I discovered on my own last year.

The claim that phi(n)/2 is a universal exponent when n is the product of 2 distinct odd primes has been around apparently but I first spotted it this morning on page 25 in Henri Cohen's A Course In Computational Algebraic Number Theory, as a second part to the well known Euler theorem.

When I made Conjecture #1 here I looked in many undergraduate and graduate texts but I couldn't find it anywhere so I naively thought that I was the first to come up with it. Especially since  here's what one of the professors that I sent it to had to say about it.