Some Some properties of the certain \(P_t\)-sets

  • Özen ÖZER Kırklareli University

Abstract

The problem of extendibility and characterization of \(P_t\)-sets is of big interest even though the problem is old, and it was started by Greek mathematician Diophantus. Let  \(t\) be an integer. A set of   \(m\) distinct positive integers  \({a_1,a_2,\dots,a_m}\) is called a \(P_t\)-set if    \(a_i a_j+t (1\leq i\leq j\leq m)\) is a perfect square whenever \(i\neq j\)  In this paper, we will investigate several numerical \(P_k\)-sets and demonstrate that they cannot be widen. Also, we will determine some of their properties using reciprocity theorem.

Published
2017-07-31
How to Cite
ÖZER, Özen. Some Some properties of the certain \(P_t\)-sets. International Journal of Algebra and Statistics, [S.l.], v. 6, n. 1-2, p. 117-130, july 2017. ISSN 2314-4556. Available at: <http://m-sciences.com/index.php?journal=ijas&page=article&op=view&path%5B%5D=1261>. Date accessed: 20 aug. 2017. doi: https://doi.org/10.20454/ijas.2017.1261.
Section
Articles