I am trying to find a conjecture apparently made by Erdős and Straus. I say apparently because I have had so much trouble finding anything information about it that I'm beginning to doubt its existence. Here it is:
Let $\phi(X)$ be a rational function over $\mathbb{Q}$ that is defined at every positive integer. If the sum $\sum \limits_{n=1}^\infty \phi(n)$ converges, it is either rational or transcendental, i.e., it is never an irrational algebraic number.
Has anyone heard of this conjecture? I was told about it by my supervisor, but he doesn't remember where he heard about it.