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A hydrologist is analyzing groundwater flow and models a particular aquifer's recharge rate as a function of time using integers. If the recharge rate at time \( t \) is given by \( R(t) = 3t^2 + 2t + 1 \), for \( t = 1, 2, 3, \ldots, 10 \), what is the greatest common divisor of all values \( R(1), R(2), \ldots, R(10) \)?
First, compute \( R(t) = 3t^2 + 2t + 1 \) for \( t = 1 \) to \( 10 \):
R(1) &= 3(1)^2 + 2(1) + 1 = 3 + 2 + 1 = 6, \\

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