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Find the number of integral solutions of $$5x^2 - 7y^2 = 9$$.
Correct Answer: 0
Work modulo 5. The equation gives $$-7y^2 \equiv 9$$, i.e. $$3y^2 \equiv 4 \pmod 5$$, so $$y^2 \equiv 8 \equiv 3 \pmod 5$$. But squares modulo 5 are only 0, 1 and 4, so this is impossible. There are 0 integral solutions.
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