Adams theorem on Bernoulli numbers revisited

✍ Scribed by R. Thangadurai

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 212 KB
• Volume: 106
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.12.006

✦ Synopsis

If we denote B n to be nth Bernoulli number, then the classical result of Adams (J. Reine Angew. Math. 85 (1878) 269) says that p c jn and ðp À 1Þ[n; then p c jB n where p is any odd prime p43: We conjecture that if ðp À 1Þ[n; p c jn and p cþ1 [n for any odd prime p43; then the exact power of p dividing B n is either c or c þ 1: The main purpose of this article is to prove that this conjecture is equivalent to two other unproven hypotheses involving Bernoulli numbers and to provide a positive answer to this conjecture for infinitely many n: