Squares in products in arithmetic progression with at most one term omitted and common difference a prime power

Laishram, Shanta ; Shorey, T. N. ; Tengely, Szabolcs (2008) Squares in products in arithmetic progression with at most one term omitted and common difference a prime power Acta Arithmetica, 135 (2). pp. 143-158. ISSN 0065-1036

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Official URL: http://journals.impan.pl/cgi-bin/doi?aa135-2-4

Related URL: http://dx.doi.org/10.4064/aa135-2-4

Abstract

It is shown that a product of k−1 terms out of k ≥ 7 terms in arithmetic progression with common difference a prime power >1 is not a square. In fact it is not of the form by2 where the greatest prime factor of b is less than or equal to k. Also, we show that product of 11 or more terms in an arithmetic progression with common difference a prime power > 1 is not of the form by2 where the greatest prime factor of b is less than or equal to pπ(k)+2.

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ID Code:67711
Deposited On:31 Oct 2011 13:29
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