Loyola University Maryland

Department of Mathematics and Statistics

Math/Stat Club Seminar

Primes, Polynomials, and

Dr. Michael Knapp

Loyola University Maryland

February 26, 2014

Room: 133 Cohn Hall


In this seminar, I'll talk about one of my new favorite theorems. If you take any positive integer, there's a natural way to turn it into a polynomial. For example 1,234 corresponds to \( 1x^3+2x^2+3x+4 \). It turns out that if the original number is prime, then the polynomial you get has no factors (with integer coefficients). I'll discuss this theorem and some extensions, including one involving the number in the title.

Note: The number 49,598,666,989,151,226,098,104,244,512,918 is pronounced
49 nonillion 598 octillion 666 septillion 989 sextillion 151 quintillion 226 quadrillion 98 trillion 104 billion 244 million 512 thousand 918.

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