Geodesic
On the sum of squares of five prime numbers one of which belongs to an arithmetic progression
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 85-96

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We study the equation $$ N=p_1^2+p_2^2+p_3^2+p_4^2+p_5^2, $$ where $p_1$, $p_2$, $p_3$, $p_4$, $p_5$ are prime numbers, $p_1+2\equiv0\pmod{k}$, $(k,2)=1$, and $N\equiv5\pmod{24}$. 
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     author = {M. B. Laporta and D. I. Tolev},
     title = {On the sum of squares of five prime numbers one of which belongs to an arithmetic progression},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {85--96},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a7/}
}
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M. B. Laporta; D. I. Tolev. On the sum of squares of five prime numbers one of which belongs to an arithmetic progression. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 85-96. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a7/