Geodesic
Sums of characters with prime numbers in an arithmetic progression
Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 485-501

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One of the corollaries of the fundamental theorem in this paper is a theorem about power residues and nonresidues $\operatorname{mod}q$ in sequences of the form $p+k$, where the prime numbers $p$ belong to the beginning of an arithmetic progression. 
@article{IM2_1971_5_3_a1,
     author = {A. A. Karatsuba},
     title = {Sums of characters with prime numbers in an arithmetic progression},
     journal = {Izvestiya. Mathematics },
     pages = {485--501},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a1/}
}
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A. A. Karatsuba. Sums of characters with prime numbers in an arithmetic progression. Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 485-501. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a1/