### Abstract

Congruences of Ankeny-Artin-Chowla type modulo p
^{2} for a cyclic subfield K of prime conductor p were derived by Jakubec and expressed in terms of a technically defined map Φ. Later, Jakubec and Lassak found a decomposition of the map Φ modulo p
^{2} and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p
^{3} was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p
^{3}, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p
^{3}. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p
^{n} which would allow a description of analogous congruences modulo p
^{n}.

Original language | English (US) |
---|---|

Pages (from-to) | 793-800 |

Number of pages | 8 |

Journal | Mathematica Slovaca |

Volume | 60 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2010 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Mathematica Slovaca*,

*60*(6), 793-800. https://doi.org/10.2478/s12175-010-0047-1

}

*Mathematica Slovaca*, vol. 60, no. 6, pp. 793-800. https://doi.org/10.2478/s12175-010-0047-1

**Decomposition of congruences involving a map Φ.** / Marko, František.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Decomposition of congruences involving a map Φ

AU - Marko, František

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Congruences of Ankeny-Artin-Chowla type modulo p 2 for a cyclic subfield K of prime conductor p were derived by Jakubec and expressed in terms of a technically defined map Φ. Later, Jakubec and Lassak found a decomposition of the map Φ modulo p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.

AB - Congruences of Ankeny-Artin-Chowla type modulo p 2 for a cyclic subfield K of prime conductor p were derived by Jakubec and expressed in terms of a technically defined map Φ. Later, Jakubec and Lassak found a decomposition of the map Φ modulo p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.

UR - http://www.scopus.com/inward/record.url?scp=78650248027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650248027&partnerID=8YFLogxK

U2 - 10.2478/s12175-010-0047-1

DO - 10.2478/s12175-010-0047-1

M3 - Article

VL - 60

SP - 793

EP - 800

JO - Mathematica Slovaca

JF - Mathematica Slovaca

SN - 0139-9918

IS - 6

ER -