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- Thread starter Poirot
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- Jan 26, 2012

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Take the equation modulo $3$, and you get:

$$y^2 \equiv x^3 - x + 5 \equiv x^3 - x + 2 \pmod{3}$$

Now FLT tells us that $x^3 \equiv x \pmod{3}$, so we get:

$$y^2 \equiv x - x + 2 \equiv 2 \pmod{3}$$

Can you finish?

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