January 2022
Intermediate to advanced
366 pages
9h 15m
English
“The mathematician Pascal admires the beauty of a theorem in number theory; it’s as though he were admiring a beautiful natural phenomenon. Its marvellous, he says, what wonderful properties numbers have. It’s as though he were admiring the regularities in a kind of crystal.”
– Ludwig Wittgenstein
In this chapter we have studied another important aspect of modular arithmetic called primitive root. To study primitive roots we have introduced the concept of order of an integer modulo k(∈ ℝ+). The order of an integer a modulo k is the least positive integer t for which at ≡ 1(mod k), where gcd(a, k) = 1. Basically for this value of k, a becomes the primitive root of k if t becomes ϕ(k). For instance 3 is a ...