Generalizations of Wilson's Theorem for Double-, Hyper-, Sub- and Super-factorials

Host Institution:

La Trobe University

Title of Seminar:

Generalizations of Wilson's Theorem for Double-, Hyper-, Sub- and Super-factorials

Speaker's Name:

Dr Grant Cairns

Speaker's Institution:

La Trobe University

Time and Date:

Friday 1 November, 2.00pm (AEDT)

Seminar Abstract:

Wilson's theorem, which has been known for many centuries, is a basic fact about prime numbers: it says that p is prime if and only if (p-1)!+1 is divisible by p. These days there are four standard generalizations of the factorial function: the double factorial, the hyperfactorial, the subfactorial and the superfactorial. In this talk we recall the definitions of these exotic factorial functions, and we present generalizations of Wilson's theorem for them.

This talk should be accessible to undergraduate students. It is joint work with Christian Aebi (College Calvin, Geneva, Switzerland), and has been accepted for publication in the Amer. Math. Monthly.

 

 

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