Complex sentence: In the special case that q is odd and d is even, this conjecture was proposed by Carlitz (1966) and proved by Fried-Guralnick-Saxl (1993).
Split into simpler sentences: In the special case that q is odd and d is even, this conjecture was proposed by Carlitz (1966). The Carlitz conjecture was proved by Fried-Guralnick-Saxl (1993).