Find all integer solutions of $y^2=1+x+x^2+x^3+x^4$. I tried moving $x^4$ to the other side and factoring the LHS to get $(y+x^2)(y-x^2)=(x+1)(x^2+1)$, but I don't know what to do with that, or if it's even the right thing to do. Please help me out!
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3Also: https://math.stackexchange.com/q/510292/42969. – Martin R Oct 27 '19 at 19:15
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It's been answered before, but here's a hint: For large $x$, bound the RHS by the squares of two polynomials. If you make the bounds tight enough, then no square of an integer will be able to lie in between. It will only remain to check the small $x$. – ViHdzP Oct 27 '19 at 19:22