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

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Özen ÖZER

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.

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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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