Let be a finite field of order . We prove that if is even and with then
If the dimension is odd and with , then
where denotes the set of nonzero quadratic residues in . Both results are, in general, best possible, including the conclusion about the nonzero quadratic residues in odd dimensions.
"On the quotient set of the distance set." Mosc. J. Comb. Number Theory 8 (2) 103 - 115, 2019. https://doi.org/10.2140/moscow.2019.8.103