Induction then yields the formula we have given easily. Hence, the true number we need to take out becomes x(1/q - 1/pq). However, these duplicate x/pq integers, because we counted some integers both in the prime p and prime q.
Obviously, there are x/q integers that are divisable by q and smaller than or equal to x, as the previous case. Now let's assume that q is also a prime that divides x. So the number of the integers not satisfying this must be. Obviously, there are x/p integers that are divisable by p and smaller than or equal to x. The most simple is by mathematical induction. Obtaining this formula has several methods. It was first introduced as Euler's phi function or simply the phi function before Sylvester came up with the term "totient" for the function.Įuler came up with a product formula for the totient function. The function is usually denoted as φ( n), a notation Gauss found after Euler formulated the function. 2.2 Finding a statement equivalent to being a prime.
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