### Abstract

There is a very rich literature on perfect powers or almost perfect powers in products of the form m(m + d) …: (m + (k − 1)d), where m, d are coprime positive integers and k ≥ 3. By a conjecture, such a product is never a perfect n-th power if k > 3, n ≥2 or k = 3, n > 2. In the classical case d = 1 the conjecture has been proved by Erdős and Selfridge [11]. The general case d ≥ 1 seems to be very hard, then there are only partial results; for survey papers on results obtained before 2006 we refer to Tijdeman [46]– [48], Shorey and Tijdeman [43, 44], Shorey [38]–[42]_and Győry [15, 16].

Original language | English |
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Title of host publication | Bolyai Society Mathematical Studies |

Publisher | Springer Berlin Heidelberg |

Pages | 311-324 |

Number of pages | 14 |

DOIs | |

Publication status | Published - Jan 1 2013 |

### Publication series

Name | Bolyai Society Mathematical Studies |
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Volume | 25 |

ISSN (Print) | 1217-4696 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Bolyai Society Mathematical Studies*(pp. 311-324). (Bolyai Society Mathematical Studies; Vol. 25). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-39286-3_10

**Perfect powers in products with consecutive terms from arithmetic progressions, II.** / Györy, K.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Bolyai Society Mathematical Studies.*Bolyai Society Mathematical Studies, vol. 25, Springer Berlin Heidelberg, pp. 311-324. https://doi.org/10.1007/978-3-642-39286-3_10

}

TY - CHAP

T1 - Perfect powers in products with consecutive terms from arithmetic progressions, II

AU - Györy, K.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - There is a very rich literature on perfect powers or almost perfect powers in products of the form m(m + d) …: (m + (k − 1)d), where m, d are coprime positive integers and k ≥ 3. By a conjecture, such a product is never a perfect n-th power if k > 3, n ≥2 or k = 3, n > 2. In the classical case d = 1 the conjecture has been proved by Erdős and Selfridge [11]. The general case d ≥ 1 seems to be very hard, then there are only partial results; for survey papers on results obtained before 2006 we refer to Tijdeman [46]– [48], Shorey and Tijdeman [43, 44], Shorey [38]–[42]_and Győry [15, 16].

AB - There is a very rich literature on perfect powers or almost perfect powers in products of the form m(m + d) …: (m + (k − 1)d), where m, d are coprime positive integers and k ≥ 3. By a conjecture, such a product is never a perfect n-th power if k > 3, n ≥2 or k = 3, n > 2. In the classical case d = 1 the conjecture has been proved by Erdős and Selfridge [11]. The general case d ≥ 1 seems to be very hard, then there are only partial results; for survey papers on results obtained before 2006 we refer to Tijdeman [46]– [48], Shorey and Tijdeman [43, 44], Shorey [38]–[42]_and Győry [15, 16].

UR - http://www.scopus.com/inward/record.url?scp=84898677016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898677016&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-39286-3_10

DO - 10.1007/978-3-642-39286-3_10

M3 - Chapter

AN - SCOPUS:84898677016

T3 - Bolyai Society Mathematical Studies

SP - 311

EP - 324

BT - Bolyai Society Mathematical Studies

PB - Springer Berlin Heidelberg

ER -