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 º 0(mod k), $(k,2)=1$, and $N$º 5(mod
24).

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Last modified: July 5, 2002