# 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: 16 oct. 2017. doi: https://doi.org/10.20454/ijas.2017.1261.
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