Introduction In this investigation I have been given the task of discovering a formula to tell us the value of n when 'n' is any given number. Also, in the second part of my investigation, look into whether there is a link between the phi of a number, and the product of its factors' phis. Such as: Is it true that 6 x 4 = 6 x 4? How to Find the Phi of a Number For any positive integer n, the phi function n is defined as the number of positive integers les than...
5^4 = 500

5^5 = 2500

From the prime numbers and their powers phi's it can be seen that a clear pattern has become apparent. It can be seen that each time the power goes up by 1, the phi of that powered prime, is the previous powered prime's phi, multiplied by the prime number in question. I know this because it is evident in the previously stated phi's, for example from the powers of 2 phi functions, 1 x 2 is 2, 2 x 2 is 4, 4 x 2 is 8 and so on.