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Let p be an odd prime. Assuming the Extended Riemann Hypothesis, we show how to construct O((log p) 4 (log log p) −3 ) residues modulo p, one of which must be a primitive root, in deterministic polynomial time. Granting some well-known character sum bounds, the proof is elementary, leading to an explicit algorithm.doi:10.1090/s0025-5718-97-00890-9 fatcat:6xxziawpejdsvmr4aqsi4vqnxq