# C L's number

Let $$M$$ be the smallest positive odd integer that is not a multiple of the square of any prime, and that can be expressed as a sum of squares of two integers in at least $$4$$ distinct ways, ignoring signs and order. Find the last 3 digits of $$M$$.

This problem is shared by C L.

Details and assumptions

If $$M=a^2+b^2$$, then ignoring signs and order implies $$M = (-a)^2+b^2=b^2+a^2$$ are not counted as distinct.

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