Geodesic
On the number of solutions of the equation $(x_1+\dots+x_n)^2=ax_1\dots x_n$ in the finite field $\mathbb F_q$ for $\mathrm{gcd}(n-2,q-1)=7$ and for $\mathrm{gcd}(n-2,q-1)=14$
Čebyševskij sbornik, Tome 1 (2001) no. 1, pp. 5-14

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     author = {Yu. N. Baulina},
     title = {On the number of solutions of the equation $(x_1+\dots+x_n)^2=ax_1\dots x_n$ in the finite field $\mathbb F_q$ for $\mathrm{gcd}(n-2,q-1)=7$ and for $\mathrm{gcd}(n-2,q-1)=14$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {5--14},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2001_1_1_a0/}
}
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Yu. N. Baulina. On the number of solutions of the equation $(x_1+\dots+x_n)^2=ax_1\dots x_n$ in the finite field $\mathbb F_q$ for $\mathrm{gcd}(n-2,q-1)=7$ and for $\mathrm{gcd}(n-2,q-1)=14$. Čebyševskij sbornik, Tome 1 (2001) no. 1, pp. 5-14. http://geodesic.mathdoc.fr/item/CHEB_2001_1_1_a0/