On a conjecture on Pythagorean numbers
L. Jésmanowicz conjectured that if \(u\), \(v\), \(w\) are Pythagorean numbers, then the diophantine equation on \(\ell,m,n\in\mathbb{N}\) \[ u^ \ell+ v^ m= w^ n \] has the unique solution \((\ell,m,n)= (2,2,2)\). In this paper, the authors prove this conjecture in some special cases.
scientific article; zbMATH DE number 549026