The odd-number sequence: squares and sums

Abstract

Direct study of various characteristics of integers and their interactions is readily accessible to undergraduate students. Integers obviously fall in different classes of modular rings and thus have features unique to that class which can result in a variety of formations, particularly with sums of squares. The sum of the first n odd numbers is itself the square of n within the odd number sequence, from which testing for primality within the Fibonacci sequence is investigated in this note.

Keywords:

• Fibonacci numbers
• prime numbers
• Hoppenot equation
• modular rings
• triangular numbers

AMS Classification Numbers:

• 11B39
• 11B50

Acknowledgement

We are grateful to an anonymous referee for corrections, questions and suggestions to improve this note.

Disclosure statement

No potential conflict of interest was reported by the authors.