k=1 z k ∣ ∣ ∣ ∣ ∣ = √ n (i = 2, . . . , n − 1) when n ≥ 3 is a prime power. We give explicit constructions of n-tuples (z1, . . . , zn) which we prove are global minima for these problems. These are two of the few times in Turán power sum theory where solutions in the inf max problem can be explicitly calculated.