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Mathematical Citation Quotient (MCQ) 2017: 0.20

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Squares in (12 + m 2) ⋯ (n 2 + m 2)

Pak Tung Ho
  • Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA. E-mail:
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Published Online: 2010-01-26 | DOI: https://doi.org/10.1515/INTEG.2009.057


Recently, Cilleruelo proved that the product is a square only for n = 3. In this note, using similar techniques, we prove that for the positive integer m whose divisors are of the form of 4q+1, the product is not a square for n sufficiently large. As a corollary, we prove that for is not a square for all n.

Keywords.: Quadratic polynomials; squares

About the article

Received: 2008-07-10

Revised: 2009-02-11

Accepted: 2009-09-11

Published Online: 2010-01-26

Published in Print: 2009-12-01

Citation Information: Integers, Volume 9, Issue 6, Pages 711–716, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.057.

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