On The Theory Of Perfect Numbers and Primes

This paper explores the properties of the set $\frac{n(n+1)}{2}$ and its implication on the distribution of perfect numbers. A major takeaway is a conjecture that all perfect numbers - even and odd lie on that line. It also describes primes arising from the perfect number line equation and equivalent statements of perfectness.

The abundancy index of divisors of odd perfect numbers – Part II

In this note, we show that if N = q^kn^2 is an odd perfect number with special prime q, and N is not divisible by 3, then the inequality q < n holds. We then give another unconditional proof for the inequality q < n which is independent of the results of Brown and Starni.

Securing The Predicting Data Using Rjb20 Algorithm

The current world is information world; without this information can’t make due in present stage. This information created more from web- based media; this media information is public information; This public infor- mation did not have well security; so we applying the proposed method and it has 2 steps; 1. Addition property of the matrix;2. Perfect numbers swapped. The proposed method gives well security while comparing with Salsa method.

On Triangular Secure Domination Number

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m). A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m) is called a secure domination number of graph T_m. A secure dominating number γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.