Find all integer solutions to $x^4 + 2x^3 + 2x^2 + 2x +5 = y^2$.
I'm in a dead end. I've transformed the expression in the following state: $(x^2+1)(x+1)^2 = y^2 -4$
I couldn't see anyway in which I could work with this expression in this state, so I continued into writing $(x^2+x+2)^2 - y^2 = 4x(x+1)$. Now I'm trying to use mod 8 and trying with different modulo. Please suggestions?
not entire solution tho...
Hint: $(x^2+x)^2 < y^2 < (x^2+x+1)^2$.