✦ LIBER ✦

Equal Sums of Two kth Powers

✍ Scribed by T.D. Browning

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 237 KB
Volume: 96
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2002.2800

No coin nor oath required. For personal study only.

✦ Synopsis

Let k55 be an integer, and let x51 be an arbitrary real number. We derive a bound

for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way.

📜 SIMILAR VOLUMES

Sums of Two Exact Powers

✍ Stephen D. Cohen; Zhang Wenpeng 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 109 KB

The Additive Completion of kth Powers

✍ Wenguang Zhai 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 97 KB

Let k 2 be a fixed integer. For positive integers M N, let S k (M, N) denote the set of all sets A/[0, M] such that, for all positive integers n N, n can be written as n=a+b k with a # A and b a positive integer. Define Given =>0, we prove that there exists a $>0 such that for all sufficiently larg

The Additive Completion of Kth-Powers

✍ J. Cilleruelo 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 136 KB

On Sums of Seventh Powers

✍ Ajai Choudhry 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 79 KB

On the Construction of Sets of Integers

On the Construction of Sets of Integers with Equal Power Sums

✍ M. Jacroux 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 216 KB

In this paper we give a new method for constructing sets of integers having equal th power sums. Using the method, some new results are derived concerning the Tarry-Escott Problem. i' 1995 Academic Press. Inc.

p-AdicL-Functions and Sums of Powers

✍ Lawrence C. Washington 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 379 KB

We give an explicit p-adic expansion of np j=1, ( j, p)=1 j &r as a power series in n. The coefficients are values of p-adic L-functions. 1998 Academic Press Several authors (see [2, pp. 95 103]) have studied the sums : np j=1 ( j, p)=1 k=1 \ &r k + L p (r+k, | 1&k&r )( pn) k