On consecutive quadratic non-residues: a conjecture of Issai Schur

2003/05/21 by Patrick Hummel, Hummel, Patrick
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Limits and Structures in Graph Theory #math.NT #msc:11A15

paper · pdf · doi:10.48550/arxiv.math/0305298

8 pages

arxiv created 2003/05/21 · arxiv updated 2009/11/30

Abstract

Issai Schur once asked if it was possible to determine a bound, preferably using elementary methods, such that for all prime numbers p greater than the bound, the greatest number of consecutive quadratic non-residues modulo p is always less than the square root of p. This paper uses elementary methods to prove that 13 is the only prime number for which the greatest number of consecutive quadratic non-residues modulo p exceeds the square root of p.

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