n = 3277;
m = Floor[N[(Sqrt[n])]]

f[x_] := (x - m)^2 - n

a2 = Table[f[i], {i, -2, 2}]

r = Table[FactorInteger[a2[[i]]], {i, 1, 5}]

2^2*3*7

GCD[3277, 84 - 55*57]

Solve[{x3 + x4 + x5 == 0, x1 + x2 + x4 == 0, 
        x3 + x5 == 0, x1 == 0, x2 == 0, x4 == 0, 
        Modulus == 2}, {x1, x2, x3, x4, x5}, 
      Mode -> Modular]