方程证明

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求证：方程x²－3y²=17没有整数解

证明：设整数x按模3分类讨论，

①当x＝3k时，　　　（3k）²－3y²=17,  　　3(3k²－y²)=17

⑵当x=3k±1时，　　（3k±1）²－3y²=17    3⁽3k²±2k－y²)=16

由①②左边的整数是3的倍数，而右边的17和16都不是3的倍数，

　∴上述等式都不能成立，因此，方程x²－3y²=17没有整数解