The Number of Extended k-th Power Residues mod pm

Kenji KOYAMA

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Kenji KOYAMA, "The Number of Extended k-th Power Residues mod pm" in IEICE TRANSACTIONS on transactions, vol. E69-E, no. 12, pp. 1267-1270, December 1986, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e69-e_12_1267/_p

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@ARTICLE{e69-e_12_1267,
author={Kenji KOYAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={The Number of Extended k-th Power Residues mod pm},
year={1986},
volume={E69-E},
number={12},
pages={1267-1270},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={December},}

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TY - JOUR
TI - The Number of Extended k-th Power Residues mod pm
T2 - IEICE TRANSACTIONS on transactions
SP - 1267
EP - 1270
AU - Kenji KOYAMA
PY - 1986
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E69-E
IS - 12
JA - IEICE TRANSACTIONS on transactions
Y1 - December 1986
AB - 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.
ER -