Curious Patterns and Identities Involving Consecutive Integers

Authors

• Carlo Cattani
• Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

8-10-2026

Abstract

Consecutive integers exhibit numerous surprising patterns and elegant identities. In this article, we investigate several classical properties involving products, sums, divisibility, perfect squares, cubes, pronic numbers, triangular numbers, sums of squares, and Pythagorean triples. Using only elementary algebra, symmetry arguments, and mathematical induction, we establish a collection of identities that reveal rich connections among these classical topics. The exposition is intended for students, teachers, and recreational mathematicians, illustrating how simple observations about consecutive integers can lead to beautiful mathematical patterns and deeper insights into elementary number theory.

Comments

Copyright (c) 2026 Carlo Cattani, Mrinal Kanti Roychowdhury (Author)

Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Cattani, Carlo, and Mrinal Kanti Roychowdhury. "Curious Patterns and Identities Involving Consecutive Integers." ISQGD Recreational Mathematics Journal 1, no. 1 (2026). https://doi.org/10.67239/rmj.v01.n01.a004

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

ISQGD Recreational Mathematics Journal

DOI

10.67239/rmj.v01.n01.a004