On the properties of Newton–Euler pairs

✍ Scribed by Zhi-Hong Sun

• Book ID: 104024601
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 344 KB
• Volume: 114
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2005.05.004

✦ Synopsis

If {a n } ∞ n=1 and {b n } ∞ n=1 are two sequences such that a 1 =b 1 and b n +a

, then we say that (a n , b n ) is a Newton-Euler pair. In the paper, we establish many formulas for Newton-Euler pairs, and then make use of them to obtain new results concerning some special sequences such as p(n), (n) and B n , where p(n) is the number of partitions of n, (n) is the sum of divisors of n, and B n is the nth Bernoulli number.