**x^2 + 3xy + 2*911x + 2*911y +911^2 = 0. **
Solve the bolded equation for an integer couple (x,y)

I was hoping to find an elegant trick using x+y+911, but nope. At least the equation can be solved for y without radicals.

y = -(3x+3644)/9 - (829921/(3x+1822))/9

829921 has six integer factors: 1, -1, 911, -911, 829921, -829921. Equating each of these to 3x+1822 yields three integer possibilities for x: -607, -911, and 276033. This in turn yields three integer couples **(-607,-92416), (-911,0), and (276033,-92416)**.