The T₄ and G₄ constructions of Costas arrays

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We examine two particular constructions of Costas arrays known as the Taylor variant of the Lempel construction, or the T₄ construction, and the variant of the Golomb construction, or the G₄ construction. We connect these constructions with the concept of Fibonacci primitive roots, and show that under the Extended Riemann Hypothesis the T₄ and G₄ constructions are valid infinitely often.