2024 and Differences of Squares

Published by MrHonner on

The new year is one of my favorite kinds of numbers: a difference of squares!

2024 = 46 \times 44 = (45 + 1) \times (45 - 1) = 45^2 - 1^2

This observation got me thinking about what kinds of numbers can be written as the difference of squares. For example, 3 = 2^2 - 1^2, 5 = 3^2 - 2^2, and 16 = 4^2 - 0^2, but it is impossible to write 6 as the difference of squares of integers.

So here’s a little mathematical puzzle to start the new year: Is there a largest number that can not be expressed as the difference of squares? If so, find it. If not, prove no such number exists. Good luck, and happy new year! I’ll give my answer in a follow-up post.

Related Posts

Related Post

Categories: ChallengeNumbers

0 Comments

Leave a Reply

Your email address will not be published. Required fields are marked *

Related Posts

Challenge Numbers

2024 and Differences of Squares — Solution

The new year 2024 is a difference of squares, , which got me thinking about a fun little number theory problem: Is there a largest number that can not be expressed as the difference of Read more…

Numbers Resources Teaching Writing

Pierre de Fermat’s Link to a High School Student’s Prime Math Proof — Quanta Magazine

My latest column for Quanta Magazine tells the mathematical story of the incredible high school student who proved a result about not-quite prime numbers that had eluded mathematicians for decades. [Daniel] Larsen was a high Read more…

Numbers Resources Teaching

The Symmetry That Makes Solving Math Equations Easy — Quanta Magazine

My latest column for Quanta Magazine is about one of the most dreaded mathematical objects in high school math: the quadratic formula! As complicated as the quadratic formula is, the cubic formula is much worse, Read more…

Follow

Get every new post delivered to your Inbox

Join other followers: