Abstract: In this article, two varieties of 3-tuples {ℳ,𝒩,𝒪} and {𝒜,ℬ,𝒞} with the objects are some renowned numbers composed with the conditions that ℳ−𝒩,ℳ−𝒪,𝒩−𝒪 and 𝒜2+ℬ, 𝒜2+𝒞,ℬ2+𝒞 remains square numbers are estimated. Also, it is proved that such 3-tuples cannot be prolonged to 4-tuples with the assistance of properties of congruence relations.