Jacobsthal sum

In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by Jacobsthal (1907).

The Jacobsthal sum is given by

${\displaystyle \phi _{n}(a)=\sum _{m{\bmod {p}}}\left({\dfrac {m(m^{n}+a)}{p}}\right)}$

where p is prime and () is the Legendre symbol.