Number

• The Phi Function
  For any positive integer, n, the Phi Function of n is defined as the number of positive integers less than n which have no factor (other than 1) in common (are co-prime) with n.
  Examples of co-prime pairs (ones that share no common factors) are are the numbers 3 and 5, 4 and 7, 8 and 15. Clearly, no two even numbers can be a co-prime pair.
  Some interesting and accesible results can be found, at least through experimentation, at secondary school level. For example: is there a connection between the following forms

for a variety of choices of m and n.
What if the argument to the function is a prime number, or a power of a prime number ?

Well, hopefully my Phi Function Calculator (A Visual Basic Executable File) could help you to eek out these and other more esoteric results.
Note that the file Msvbvm60.dll is required to run the Phi Function Calculator. If you don't have it then click here for a self-extracting zip of it (717 KB). Be sure to place it in your C:\Windows\System directory.
Have fun!

• Countdown
  This is a Visual Basic program that I wrote as a mental arithmetic exercise for the maths classroom. Click here to go to page
  

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