NEW THEOREMS ON A QUADRATIC SUM SEQUENCE DERIVED FROM FOUR CONSECUTIVE NATURAL NUMBERS

Abstract

In this paper, we study a quadratic sequence defined as the sum of the squares of four consecutive natural numbers. While this sequence mentioned in some online platforms where a few of itsproperties like parity and non-squareness discussed, we present new theorems that provide additional arithmetic and modular properties. Moreover, we connect our study to the classical Lagrange’s Four Squares Theorem. A thorough exploration of periodicity, divisibility, and modular behavior is included.