The research article “On a Problem of Erdős and Graham”, co-authored by METU member Assoc. Prof. Erhan Gürel, has been published in Bulletin of the Brazilian Mathematical Society.
An old conjecture of Erdős 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.
Yıldız, B., & Gürel, E. (2020). On a problem of erdős and graham. Bulletin of the Brazilian Mathematical Society, 51(2), 397-415. doi:10.1007/s00574-019-00158-9
Article access: https://link.springer.com/article/10.1007/s00574-019-00158-9
Assoc. Prof. Erhan Gürel |
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| egurel@metu.edu.tr | Scopus Author ID: 26659014700 |
| About the author |
Tags/Keywords:
Hypersurfaces, Integer points, Parametrizations, Polynomials
Other authors:
Yıldız, B.
