It is well-known that for $p=1, 2, 3, 7, 11, 19, 43, 67, 163$, the class number of Q(√-p) is one. We use this fact to determine all the solutions of x²+pᵐ=4yⁿ in non-negative integers $x, y, m$ and n.
No takes yet. Share an insight, caveat, or question.
Chakraborty et al. (2020) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: