IDEAS home Printed from https://ideas.repec.org/a/bcp/journl/v9y2025i2p771-780.html
   My bibliography  Save this article

Difference of Squares of Two Consecutive Even Numbers: A Mathematical Investigation

Author

Listed:
  • Ronald S. Decano

    (Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City)

  • Jernel C. Ondong

    (Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City)

  • Liezel P. Vasay

    (Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City)

  • Greatchen L. Medrano

    (Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City)

Abstract

This study investigates the difference of squares between two consecutive even numbers using the formula 4(n+1), derived from the general identity a2−b2 = (a−b) of (a+b). The research aims to uncover more profound insights into this formula’s mathematical properties, sequence behavior, and divisibility characteristics. The study adopts theoretical and computational approaches that validate the formula for fifteen examples of consecutive even numbers. The formula 4(n+1) has been validated for a wide range of even numbers, and its results match the manually computed difference of squares (2n+2)2−(2n)2. For all even 2n, the difference of squares simplifies to 4(n+1), confirming the formula’s accuracy and consistency. The formula 4(n+1) provides valuable insights into number patterns, such as divisibility and arithmetic sequences, highlighting its importance in solving mathematical problems. Its simplicity also makes it a powerful tool for teaching foundational concepts and exploring connections across various areas of mathematics.

Suggested Citation

  • Ronald S. Decano & Jernel C. Ondong & Liezel P. Vasay & Greatchen L. Medrano, 2025. "Difference of Squares of Two Consecutive Even Numbers: A Mathematical Investigation," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 9(2), pages 771-780, February.
    • Handle: RePEc:bcp:journl:v:9:y:2025:i:2:p:771-780
    as

    Download full text from publisher

    File URL: https://www.rsisinternational.org/journals/ijriss/Digital-Library/volume-9-Issue:2/771-780.pdf
    Download Restriction: no
    File URL: https://rsisinternational.org/journals/ijriss/articles/difference-of-squares-of-two-consecutive-even-numbers-a-mathematical-investigation/
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bcp:journl:v:9:y:2025:i:2:p:771-780. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Dr. Pawan Verma (email available below). General contact details of provider: https://rsisinternational.org/journals/ijriss/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.