On a conjecture on Pythagorean numbers. II
In the paper reviewed above, the authors considered the following diophantine equation on \(\ell,m,n\in\mathbb{N}\), \[ (4a^ 2- y^ 2)^ \ell+ (4 ay)^ m= (4 a^ 2+ y^ 2)^ n, \tag{1} \] where \(a,y\in\mathbb{N}\) with \((a,y)=1\), \(2a>y\), \(y\equiv 3\pmod 4\). In this paper, they consider the case \(y=3\). They prove that in some cases, the only solution of (1) is \((\ell,m,n)= (2,2,2)\).
scientific article; zbMATH DE number 549034