# A new algorithm for computing the partial-sums of `ϕ(k)`, for `1 <= k <= n`: # Sum_{k=1..n} phi(k) # where phi(k) is the Euler totient function. # Based on the ...

In this paper, we show that when\(N_k\) is a primorial and \(\varphi(N_k)\)is Euler’s totient function, the inequality \(\varphi(N_k) < \frac{N_k}{e^{\gamma}\log ...

Abstract: In this paper, an attempt is made to apply the Euler's Totient function and Euler's theorem to organizing calculations of the period of the modular exponentiation function inspired by Shor's ...

# Input the number for which you want to calculate Euler's Totient Function n = int(input("Enter a positive integer (n) to calculate Euler's Totient Function: ")) ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

This is a preview. Log in through your library . Abstract Carmichael's conjecture states that if φ(x) = n, then φ(y) = n for some y ≠ x (φ is Euler's totient function). We show that the conjecture is ...