EPaDel Spring 2025 Section Meeting

Wing Hong Tony Wong
Kutztown University
A Journey Into the Fun of Number Theory with Niven Numbers

A positive integer n is called a Niven number if the sum of its digits divides n. For example, 18 is a Niven number since 1+8=9 and 9 divides 18. In contrast, 19 is not a Niven number since 1+9=10 and 10 does not divide 19. In this talk, we investigate the maximum number of consecutive Niven numbers and extend our discussions to arithmetic progressions. Additionally, we explore related concepts and present several potential directions for future research.

Paul Schwartz
Stevens Institute of Technology
Fermat's Last Theorem and its Lasting Impact on Mathematics

Fermat's Last Theorem states that when n >= 3 there are no positive integers a, b and c such that a^n + b^n=c^n. Though this statement of Fermat's is easy to read, it turned out to be exceedingly difficult to prove. Prior to its completion in 1994, the search for proof of Fermat's statement spent centuries in the spotlight as the most difficult problem in mathematics, attracting the attention of many of the most brilliant mathematical minds the world has ever known. We will examine the three-hundred-year struggle to prove Fermat's Last Theorem, the mathematical titans who tried, and the series of surprising circumstances that made person after person interested in solving the problem.

David Nacin
William Paterson University
Padovan, Pascal, and Proofs without Words

What happens when we attempt to construct the Fibonacci spiral using triangles instead of squares? We get a new sequence: the Padovan sequence, which answers its own set of unique and beautiful counting problems. In this talk, we will demonstrate how this construction defines the sequence and then rediscover it in other, possibly surprising, places. We will also prove several identities without using words or numbers by considering triangles composed of colored dots. The Fibonacci sequence is connected to the golden ratio, which arises from a simple question about rectangles and proportion. A slightly different, natural question leads to a new ratio and another method for defining our sequence. We will then explore the uses of this sequence and its ratio in architecture and discuss the history behind the patterns we have uncovered. We conclude with a counterexample to a conjecture about this sequence, which leads us to a final construction involving copies of the Fibonacci sequence itself.

David Nacin is a professor of mathematics at William Paterson University, where he also serves as director of their graduate program in Applied Mathematics. He received his Ph.D. from Rutgers University in 2005 under the guidance of Dr. Robert Wilson. His research interests include non-commutative algebra, discrete mathematics, and recreational mathematics. A Python enthusiast, David employs coding extensively for research, teaching, and personal enjoyment. He also enjoys cooking, hiking, and many varieties of games. David enjoys designing and studying puzzles related to partition identities, the motion of chess pieces, finite groups, and other mathematical structures. Author of the book Math-Infused Sudoku, published by the American Mathematical Society in 2019, his mathematical puzzles have appeared in many magazines and academic journals. His second book, The Group Theory Puzzle Book, is being released by Springer this Fall. Since the year 2016 he has maintained a puzzle blog at quadratablog.blogspot.com.

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