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

✍ Scribed by Patrick Hummel

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 212 KB
• Volume: 103
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.06.003

✦ Synopsis

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 p 1=2 : 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 p 1=2 :