ON THE SOME PARTICULAR SETS

Abstract

For 𝑡 an integer, a 𝑃𝑡 set is defined as a set of 𝑚 positive integers with the property that the product of its any two distinct element increased by 𝑡 is a perfect square integer.

In this study, the certain special 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 sets with size three are considered. It is demonstrated that they cannot be extended to 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 with size four. Also, some properties of them are proved.

Keywords

• 𝑃𝑡 Sets,Congruences,Reciprocity

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