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March 28, 2017

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Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x3−ax2+a2b3x+9a2b2 has roots r, s, and t.

Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k2, compute the maximum possible value of ab.

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    34

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    775

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