<s>[INST] Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square. Integer values of $x$ for which $\bf{x^4+x^3+x^2+x+1}$ is a Perfect Square.
$\underline{\bf{My\; Try}}$:: Let $\bf{x^4+x^3+x^2+x+1 = k^2}$, where $k\in \mathbb{Z}$
$4x^4+4x^3+4x^2+4x+1 = 4k^2 = (2k)^2$
Now How can I proceed after that
Help Required,
Thanks
 [/INST] Hint: For all but finitely many integer values of $k$, we have
$$ (2k^2 + k)^2 < 4k^4 + 4k^3 + 4k^2 + 4k + 4 < (2k^2 + k + 2 ) ^ 2 $$
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