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Does there exist a set of $n$ points $p_1,p_2,...,p_n$ in the plane, all at mutual integer distances to each other, and an $e>0$, such that the following statement holds:

For all $a,b$ with $a^2+b^2, there exists an integer $i$, with $1\leq i\leq n$, such that the distance from $(a,b)$ to $p_i$ is irrational.

What is the least such $n$?

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    I asked this here http://mathoverflow.net/questions/90454/least-cardinality-of-a-set-of-points-in-the-plane2012-03-07

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