## Pell equation : x^2 – 313*y^2 = ± 1

$x^2 \; - \; 313 \, y^2 \; = \; \pm 1$

$32188120829134849^2 \; - \; 313\times 1819380158564160^2 \; = \; 1$

$2072150245021969438104715652505601^2 - 313\times 117124856755987405647781716823680^2 = 1$

$126862368^2 \; - \; 313\times 7170685^2 \; = \; -1$

$8166922459708340797787232^2 \; - \; 313\times 461621750415329642232445^2 \; = \; -1$