Pythagorean triples and quadratic residues modulo an odd prime
Keyword(s):
<abstract><p>In this article, we use the elementary methods and the estimate for character sums to study a problem related to quadratic residues and the Pythagorean triples, and prove the following result. Let $ p $ be an odd prime large enough. Then for any positive number $ 0 < \epsilon < 1 $, there must exist three quadratic residues $ x, \ y $ and $ z $ modulo $ p $ with $ 1\leq x, \ y, \ z\leq p^{1+\epsilon} $ such that the equation $ x^2+y^2 = z^2 $.</p></abstract>
Keyword(s):
Keyword(s):
Two-dimensional multiplicative arrays over Zq−1 and girth-6 q-ary QC-LDPC codes based on quadratic-residues modulo p
2011 ◽
Vol 65
(12)
◽
pp. 1069-1072
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1984 ◽
Vol 18
(3)
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pp. 391-395
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