A Note on the Particular Set with Size Three

Özen Özer


For a fixed integer k, a Pk  – set is defined as a set of n positive integers { x1, x2, x3,..., xn} with the property that xi, xj + k is a perfect square, whenever i j . In this paper, we prove P11 = {1,14,25}, P−11 = {1,15,36}, and P−11{4,9,23} sets cannot be extendable. It is also proved that P11 sets don’t contain any multiple of 3 and P11 sets don’t include any multiple of 7. Moreover, it is demonstrated that all of the elements of the sets P11 of size three cannot be odd positive integer. Mathematics Subject Classifications: 11A07, 11D45, 11A15.


Congruences, Pk sets, Pell’s equations, Legendre symbol.

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DOI: 10.7250/bfpcs.2016.009


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