On counterexamples to Mordell's Pellian Equation Conjecture and the AAC-Conjecture: a non-computer based approach

In this note, we discuss recently discovered counterexamples to Mordell’s Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell’s Pellian Equation Conjecture that can be checked with marginal computer assistance.