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happy new year

I have this statement: "By quadratic reciprocity there are the integers $a$ and $b$ such that $(a,b)=1$, $(a-1,b)=2$, and all prime $p$ with $p\equiv a$ (mod $b$) splits in $K$ (where $K$ is a real quadratic field)".

I have tried with many properties of quadratic reciprocity but couldn't even get to the first conclusion.

Thank you very much in advance, for any idea or advice for approach the problem

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    I'm confused. For the first conclusion, just take $b=2$ and $a$ to be odd. (Also, I think there needs to be some more quantifiers here. Are you talking about a *specific* quadratic field $K$? Or *some* quadratic field?)2012-01-05
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    Sorry, the first condition is trivial but the i need fulfilled the three conditions at the same time and for all real quadratic field Thanks2012-01-05

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