Let p be a prime ≡ 1 (mod16).
We obtain extensions of known congruences involving parameters of bioctic Jacobi
sums (modp). These extensions are used to give an elementary proof of an
important congruence of Hasse relating parameters of quartic and octic Jacobi
sums (modp). This proof leads directly to an elementary resolution of sign
ambiguities of parameters of certain quartic, octic, and bioctic Jacobi and
Jacobsthal sums. E. Lehmer’s work on ambiguities in quartic sums is thereby
extended.