Monday, 30 September 2013

Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.

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

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