More generally, the Hasse principle allows deciding whether a homogeneous Diophantine equation of degree two has an integer solution, and computing a solution if there exist.
mORE genErAlLY, the hasse pRinCiPlE aLloWs dEcIDing WhEther a HOMogEnEOuS dioPhaNTIne equatiOn of dEgree tWo hAs an iNtegeR SolUtIoN, anD cOMpuTIng a solUtion if THeRe exist.