It counts the number of positive integers less than or equal to n that have at least one prime factor in common with n. The cototient of n is defined as n − φ( n). The Cayley graph associated with Euler Totient function is called an Euler Totient Cayley graph and in this paper we study the matching domination. Jordan's totient is a generalization of Euler's. Sylvester coined the term totient for this function, so it is also referred to as Euler's totient function, the Euler totient, or Euler's totient. Thus, it is often called Euler's phi function or simply the phi function. The now-standard notation φ( A) comes from Gauss's 1801 treatise Disquisitiones Arithmeticae, although Gauss didn't use parentheses around the argument and wrote φA. A graph of the number of solutions of Lemoines Conjecture for odd numbers up to 6000. This definition varies from the current definition for the totient function at D = 1 but is otherwise the same. The counts of the number of solutions for 1,3,5,7. A generalization of Eulers totient is the Schemmel totient function (see 103). In a 1784 publication, Euler studied the function further, choosing the Greek letter π to denote it: he wrote πD for 'the multitude of numbers less than D, and which have no common divisor with it'. 4 Enumeration problems on congruences, directed graphs, magic squares. Contents 1 History, terminology, and notation 2 Computing Eulers function 2.1 Eulers product formula 2.1.1 (n) is multiplicative 2.1.2 (pk) pk pk 1 pk 1(p 1) 2.1.3 Example 2.2 Fourier transform 2. However, he did not at that time choose any specific symbol to denote it. The totient function also plays a key role in the definition of the RSA encryption system. Leonhard Euler introduced the function in 1763.

Graph of euler totient function