## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Nonexistence Conditions of a Solution for the Congruence $x^k_1 + \cdots + x^k_s \equiv N (mod p^n)$

Hiroshi Sekigawa and Kenji Koyama
Mathematics of Computation
Vol. 68, No. 227 (Jul., 1999), pp. 1283-1297
Stable URL: http://www.jstor.org/stable/2584963
Page Count: 15
Preview not available

## Abstract

We obtain nonexistence conditions of a solution for of the congruence x$^k_1 + \cdots + x^k_s \equiv N (\mod p^n)$, where k ≥ 2, s ≥ 2 and N are integers, and pn is a prime power. We give nonexistence conditions of the form (s, N mod pn) for k = 2, 3, 4, 5, 7, and of the form (s, pn) for k = 11, 13, 17, 19. Furthermore, we complete some tables concerned with Waring's problem in p-adic fields that were computed by Hardy and Littlewood.

• 1283
• 1284
• 1285
• 1286
• 1287
• 1288
• 1289
• 1290
• 1291
• 1292
• 1293
• 1294
• 1295
• 1296
• 1297