multiplicative-order

For S(f) = { n : rad(n) divides f(n) }, entire congruence classes of primes divide no element at all: none of S(sigma*_2) is divisible by a prime 3 mod 4, none of S(Phi_3) by a prime 2 mod 3. Also: exactly 1/4 of triples of primes 3 mod 4 are realizable in S(sigma*), against no pair.

Exact rational values for the proportion of k-element sets of primes admitting exponents that place them inside S(sigma*) = { n : rad(n) | sigma*(n) }: 31/72 for pairs, 15590837/30623040 for triples, and new values for k = 4 and k = 5, with the structure of the denominators explained.

🔢 This repository contains easy-to-follow Number Theory problems solved using MATLAB.

Implementation of Shor's quantum algorithm for integer factorization