The Number of Extended k-th Power Residues mod p^m

Kenji KOYAMA

Summary :

Let N(k,p^m) be the number of distinct values of x^k mod p^m for all integers x(0xp^m-1). Given a random integer a, the probability that x^ka(mod p^m) has an integer solution x is given by N(k,p^m)/p^m. Explicit and simple representations of N(k,p^m) are obtained. Asymptotic formulas of the probability N(k,p^m)/p^m as m,p and k are also shown.

• Publication: IEICE TRANSACTIONS on transactions Vol.E69-E No.12 pp.1267-1270
• Publication Date: 1986/12/25
• Type of Manuscript: LETTER
• Category: Mathematics, Combinatorics and Graph Theory

Authors

Kenji KOYAMA

Keyword