  Let n > 1 be an integer, and let F denote a field of p elements for a prime p
= 1 (mod n). By 2015, the question of existence or nonexistence of n-th power
residue difference sets in F had been settled for all n < 24. We settle the
case n = 24 by proving the nonexistence of 24-th power residue difference sets
in F. We also prove the nonexistence of qualified 24-th power residue
difference sets in F. The proofs make use of a Mathematica program which
computes formulas for the cyclotomic numbers of order 24 in terms of parameters
occurring in quadratic partitions of p.
