Lamʼs power residue addition sets

Classical n-th power residue difference sets modulo p are known to exist for n=2,4,8. During the period 1953-1999, their nonexistence has been proved for all odd n and for n=6,10,12,14,16,18,20. In 1976, Lam showed that qualified n-th power residue difference sets modulo p exist for n=2,4,6, and he proved their nonexistence for all odd n and for n=8,10,12. We further prove their nonexistence for n=14,16,18,20.