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On a Problem of Erdos and Graham
Date
2020-06-01
Author
Yildiz, Burak
Gurel, Erhan
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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An old conjecture of Erdos and Graham states that only finitely many integer squares could be obtained from product of disjoint blocks of consecutive integers of length greater than or equal to four. It is known by counterexamples that the conjecture is false for product of disjoint blocks of four and five consecutive integers. In this paper, we present new algorithms generating new polynomial parametrizations that extend the polynomial parametrization given by Bennett and Luijk (Indag Math (N.S.) 23(1-2):123-127, 2012). Moreover, we produce the first examples of integer squares obtained from product of disjoint blocks of consecutive integers such that each block has length six or seven.
Subject Keywords
General Mathematics
URI
https://hdl.handle.net/11511/64849
Journal
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
DOI
https://doi.org/10.1007/s00574-019-00158-9
Collections
Natural Sciences and Mathematics, Article