# How to prove that the equation $x^2-3y^2=17$ has no integer solutions?

How to prove that the equation $$x^2-3y^2=17$$ has no integer solutions? Can you help me?

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–  lab bhattacharjee Jan 13 at 13:05
@Ayman Hourieh Thanks a lot! –  Dao yi Peng Jan 13 at 13:14
$$x^2-3y^2=17\implies x^2\equiv2\pmod 3$$
but $x$ can be $\equiv 0,\pm1\pmod 3\implies x^2\equiv0,1\pmod 3$