On a Problem of Erdős and Graham

Üniversitemiz öğretim üyelerinden Doç. Dr. Erhan Gürel’in yazarları arasında bulunduğu “On a Problem of Erdős and Graham” başlıklı makale Bulletin of the Brazilian Mathematical Society’de yayınlandı.

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

Makaleye erişim için: https://link.springer.com/article/10.1007/s00574-019-00158-9

Etiketler/Anahtar sözcükler:

Hypersurfaces, Integer points, Parametrizations, Polynomials

Diğer Yazarlar:
Yıldız, B.