FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 1, PAGES 85-96

On the sum of squares of five prime numbers one of which belongs to an arithmetic progression

M. B. S. Laporta
D. I. Tolev

Abstract

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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, $p_1+2 \equiv 0 \pmod{k}$, $(k,2)=1$, and $N \equiv 5 \pmod{24}$.

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Last modified: July 8, 2002