Integral points on the unit circle
The author gives a complete solution to the following problem, posed by Dipendra Prasad: Determine all algebraic number fields \(K\) in which there are integers \(x\) and \(y\) such that \(x^2+y^2=1\). The proof is based on the observation that the numbers \(x\pm iy\) must be units in \(K\) or \(K(i).\)
solution of \(x^2+y^2=1\) in algebraic integers
scientific article; zbMATH DE number 1787786