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On arithmetic progressions of equal lengths with equal products

Published online by Cambridge University Press:  24 October 2008

N. Saradha ,
T. N. Shorey  and
R. Tijdeman
N. Saradha
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
T. N. Shorey
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
R. Tijdeman
Affiliation:
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
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Abstract

It is shown that apart from

there are only finitely many arithmetic progressions with given differences of equal lengths ≥ 2 and with equal products and that they can be effectively determined.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 2 , March 1995 , pp. 193 - 201
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Erdős, P.. On consecutive integers. Nieuw Arch. Wiskunde, Ser. 3 3 (1955), 124–128.Google Scholar
[2]Erdős, P.. On the product of consecutive integers III. Indag. Math. 17 (1955), 85–90.CrossRefGoogle Scholar
[3]Gabovič, Ya.. On the arithmetic progressions with equal products of terms (Russian), Colloq. Math. 15 (1966), 45–48.Google Scholar
[4]P, Problèmes543 et P 545, R1. Colloq. Math. 19 (1968), 179–180.Google Scholar
[5]Saradha, N. and Shorey, T. N.. On the equation (x + 1) … (x + k) = (y + 1) … (y + mk), Indag. Math. N.S. 3 (1992), 79–90.CrossRefGoogle Scholar
[6]Saradha, N. and Shorey, T. N.. On the equations x(x + d) … (x + (k – 1)d) = y(y + d) … (y + (mk – 1)d), Indag. Math. N.S. 3 (1992), 237–242.CrossRefGoogle Scholar
[7]Saradha, N. and Shorey, T. N.. On the equation x(x + d 1) … (x+(k – 1)d 1) = y(y + d 2) … (y + (mk – 1)d 2), Proc. Indian Acad. Sei. (Math. Sci.) 104 (1994), 1–12.CrossRefGoogle Scholar
[8]Shorey, T. N.. On the ratio of values of a polynomial. Proc. Indian Acad. Sei. (Math. Sci.) 93, (1984), 106–116.Google Scholar
[9]Störmer, C.. Quelques théorèmes sur l'équation de Pell x 2 – dy 2 = ± 1 et leurs applications. Vid. Skr. I. Math. Natur. Kl. (Christiana) 1897 No. 2, 48 pp.Google Scholar