### Abstract

In our paper a survey is given on the title equation. General finiteness theorems, bounds on n and the number of solutions, complete solution for small values of k, and some generalizations and analogues are presented. The basic ideas of the most important proofs are also outlined. We note that in the proofs of the recent results virtually every technique of modern Diophantine analysis has been employed.

Original language | English |
---|---|

Pages (from-to) | 403-414 |

Number of pages | 12 |

Journal | Publicationes Mathematicae |

Volume | 62 |

Issue number | 3-4 |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

- Bernoulli polynomials
- Superelliptic equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

^{k}+ 2

^{k}+ ... + x

^{k}= y

^{n}

*Publicationes Mathematicae*,

*62*(3-4), 403-414.

**On the equation 1 ^{k} + 2^{k} + ... + x^{k} = y^{n}
.** / Györy, K.; Pintér, Á.

Research output: Contribution to journal › Article

^{k}+ 2

^{k}+ ... + x

^{k}= y

^{n}',

*Publicationes Mathematicae*, vol. 62, no. 3-4, pp. 403-414.

^{k}+ 2

^{k}+ ... + x

^{k}= y

^{n}Publicationes Mathematicae. 2003;62(3-4):403-414.

}

TY - JOUR

T1 - On the equation 1k + 2k + ... + xk = yn

AU - Györy, K.

AU - Pintér, Á

PY - 2003

Y1 - 2003

N2 - In our paper a survey is given on the title equation. General finiteness theorems, bounds on n and the number of solutions, complete solution for small values of k, and some generalizations and analogues are presented. The basic ideas of the most important proofs are also outlined. We note that in the proofs of the recent results virtually every technique of modern Diophantine analysis has been employed.

AB - In our paper a survey is given on the title equation. General finiteness theorems, bounds on n and the number of solutions, complete solution for small values of k, and some generalizations and analogues are presented. The basic ideas of the most important proofs are also outlined. We note that in the proofs of the recent results virtually every technique of modern Diophantine analysis has been employed.

KW - Bernoulli polynomials

KW - Superelliptic equations

UR - http://www.scopus.com/inward/record.url?scp=0037908859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037908859&partnerID=8YFLogxK

M3 - Article

VL - 62

SP - 403

EP - 414

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -