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

  • Özen ÖZER Kırklareli University


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.

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: <>. Date accessed: 20 aug. 2017. doi: