# Can a^2 = 2b^2 have a solution where a, b are in Z but not zero? [duplicate]

Possible Duplicate:
How can you prove that the square root of two is irrational?

Can $a^2 = 2b^2$ have a solution where $a, b$ are in $\mathbb{Z}$ but not zero?

$\mathbb{Z}$ = positive and negative whole numbers

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## marked as duplicate by Eric Naslund, Gerry Myerson, Hans Lundmark, JavaMan, lhfNov 7 '11 at 11:40

If you can solve $a^2=2b^2$, then $$2=\left(\frac{a}{b}\right)^2$$ which means that the square root of $2$ is rational. See the linked page for some proofs that this is impossible. – Eric Naslund Nov 7 '11 at 11:34
$|a|=\sqrt{2} \cdot |b|$