For odd prime powers q with θ_q ≤ 1/3 (except six small cases), F_q always contains a pair of consecutive elements that are neither squares nor primitive.
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Consecutive non-square non-primitive pairs in a finite field
For odd prime powers q with θ_q ≤ 1/3 (except six small cases), F_q always contains a pair of consecutive elements that are neither squares nor primitive.