An existence theorem for cyclic triplewhist tournaments Original Research Article

We show that a Z-cyclic triplewhist tournament TWh(v) exists whenever v=p1α1 ⋯ prαr where the primes pi are ≡ 5 (mod 8), pi ⩾ 29. The method of construction uses the existence of a primitive root ω of each such pi (≠61) such that ω2 ±ω+1 are both squares (mod pi).