Geodesic
The reckoning of certain quartic and octic Gauss sums
Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 153-155

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In this brief note, we evaluate certain quartic and octic Gauss sums with the use of theorems on fourth and eighth power difference sets. We recall that a subset H of a finite (additive) abelian group G is said to be a difference set of G [5, p. 64] if for some fixed natural number λ, every nonzero element of G can be written as a difference of two elements of H fin exactly λ ways. 
Berndt, Bruce C.; Chowla, S. The reckoning of certain quartic and octic Gauss sums. Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 153-155. doi: 10.1017/S0017089500003190
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