Crypto stanford number theory

crypto stanford number theory

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Why do prime numbers make these spirals? - Dirichlet�s theorem and pi approximations
A unit g ? Z n ? is called a generator or primitive root of Z n ? if for every a ? Z n ? we have g k = a for some integer k. We write for the number of elements of Z n ?. The function is called the Euler totient function. Actually, it turns out to be convenient to have ? (1) = 1. We begin by defining how to perform basic arithmetic modulo n, where n is a positive integer. Addition, subtraction, and multiplication follow naturally from.
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The behaviour of units when they are exponentiated is difficult to study. For any system of equations like this, the Chinese Remainder Theorem tells us there is always a unique solution up to a certain modulus, and describes how to find the solution efficiently. Let us restate the Chinese Remainder Theorem in the form it is usually presented.