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444 has the property that if one adds it to double its square, it yields a perfect square. In other words for natural numbers m,nm,nm,n:
n2+n2+n=m2n^2 + n^2 + n = m^2 n2+n2+n=m2
There are four such n<106n<10^6 n<106. If 444 is the smallest nnn, what is the second smallest nnn?
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