In base $b,$ the square of the number $17_b$ is $211_b$. Find the base $b$.
17b = (1b + 7)
(1b + 7)^2 = b^2 + 14b + 49
211b = 2b^2 + 1b + 1
b^2 + 14b + 49 = 2b^2 + 1b + 1
b^2 - 13b - 48 = 0
(b - 16) ( b + 3) = 0
b - 16 = 0
b = 16
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