Date: March  8, 2018

Speaker: Dr. Thomas Johnstone (NYCCT)

Title: Is the product of any k many consecutive integers always divisible by k factorial?

Abstract: Recall that “k factorial” is defined as the product of all integers between 1 and k, inclusive. There are many examples when the product of k many consecutive integers is divisible by k factorial. For instance, if k=5, then the product of the five consecutive integers 12, 13, 14, 15, 16 is divisible by five factorial: indeed, 12*13*14*15*16=524160, which is divisible by 1*2*3*4*5=120.

In this talk, we will answer the question whether the product of k many consecutive integers is always divisible by k factorial. While this question can be answered using combinatorial arguments, we shall rely on elementary number-theoretic arguments such as basic divisibility rules only.