#### Filter Results:

- Full text PDF available (5)

#### Publication Year

1998

2009

- This year (0)
- Last 5 years (0)
- Last 10 years (2)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

In this paper, we present a particularly nice Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc.). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula in order to generate the desired sequence.

- Arthur T. Benjamin, Gregory P. Dresden
- The American Mathematical Monthly
- 2007

that is as easy as playing cards. Let Vn denote the Vandermonde matrix with (i, j)th entry vi j = x j i (0 ≤ i, j ≤ n). Since the determinant of Vn is a polynomial in x0, x1, . . . , xn , it suffices to prove the identity for positive integers x0, x1, . . . , xn with x0 ≤ x1 ≤ · · · ≤ xn . We define a Vandermonde card to possess a suit and a value, where a… (More)

- Gregory P. Dresden
- The American Mathematical Monthly
- 2004

Clearly n has degree φ(n), where φ signifies Euler’s totient function. These monic polynomials can be defined recursively as 1(x) = x − 1 and ∏i |n i(x) = xn − 1 for n > 1. The first few are easily calculated to be x − 1, x + 1, x2 + x + 1, x2 + 1, . . . . For these and other basic facts, see an algebra text such as [5]. While it might appear that the… (More)

- Gregory P. Dresden
- Math. Comput.
- 2003

For At(x) = f(x) − t g(x), we consider the set { ∑ At(α)=0 h(α) : t ∈ Q}. The polynomials f(x), g(x) are in Z[x], with only mild restrictions, and h(α) is the Weil height of α. We show that this set is dense in [d,∞) for some effectively computable limit point d.

- Gregory P. Dresden
- Math. Comput.
- 1998

We prove that the two smallest values of h(α)+h( 1 1−α )+h(1− 1 α ) are 0 and 0.4218 . . . , for α any algebraic integer. Introduction For K an algebraic number field, let Kv be the completion of K at the place v and let | |v be the absolute value associated with this completion Kv (more precise definitions are given below). For α ∈ K, we define the… (More)

- ‹
- 1
- ›