# Some Some properties of the certain $$P_t$$-sets

## 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.

## Article Details

How to Cite
ÖZER, Özen. (2017). Some Some properties of the certain $$P_t$$-sets. International Journal of Algebra and Statistics, 6(1-2), 117-130. https://doi.org/10.20454/ijas.2017.1261
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