Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation 2 2 2 2 2 x y z + = +ω in terms of polygonal numbers.

In this paper we introduce anti T-fuzzy subsemirings and anti T-product of two fuzzy sets which can be regarded as a generalization of anti fuzzy subgroups under t-norms.

In this paper we introduce the definition of intuitionistic anti fuzzy normal subrings. We also made an attempt to study the algebraic nature of intuitionistic anti fuzzy normal subrings of a ring. KeywordsIntuitionistic fuzzy subsets, intuitionstic anti fuzzy subring, intuitionistic anti fuzzy normal subrings.

In this paper we introduce the notions of (λ, µ)-anti-fuzzy subrings, studied some properties of them and discussed the product of them.

Developing number sequence based on polygonal numbers is an enthusiastic field in number theory. As tetrahedral numbers are similar to pyramids, one of the Seven wonders of the World, yields a unique copiousness in its suitability. In number theory study of pyramidal numbers vary in richness and variety. Also the study of continued fractions is a fastly developing field.